iflSS miy^ ;*■■•: W' THE PENNSYLVANIA MUSEUM OF ART LIBRARY PHILADELPHIA Call Number NK » J >0*^3pURCHASED RaHf X JiiOJsrTi\riJ'j( j-j ' J. rA^rari'n </f/. 'i/cneey . yUMfi renui/n. ftrKti /fe/'((/'/c ^ /itf^t'tt r/»- - y.r '*>v/r^ )f ■»■ V -'-i/rt/ . A,f I' 7>fi;i FRONTISPIECE EXPLAINED. To fhew in as pleafing a way as I could, the ftability of this Performance, and the fubje6t of the book in general, I have, by the figure on the right hand, reprefented Geometry ftanding on a rock, with a fcroU of diagrams in his hand, converfing with Perfpeftive, the next figure to him, who is attentive to the Principles of Geometry as the ground of his art; which art is reprefented by the frame on which he refts his hand. On the left, feated near the window, is an Artift bufy in defigning; at whofe right hand is the Genius of Drawing, prefenting the Artift with various patterns. The back figure is Architefture, meafuring the (haft of a Tufcan column ; and on the back ground is the Temple of Fame, to which a knowledge of thefe arts diredlly leads. THE CABINET-MAKER AND UPHOLSTERER'S D RAWI N G - B O O K, IN FOUR PARTS. B y THOMAS SHERATON, CABINET-MAKER: RECOMMENDED BY MANY WORKMEN OF THE FIRST ABILITIES IN LONDON WHO HAVE THEMSELVES INSPECTED THE WORK. THE THIRD EDITION, REVISED, AND THE WHOLE EMBELLISHED WITH 122 ELEGANT COPPER-PLATES, LONDON: PRINTED BY T. BENSLEY, BOLT COURT, FLEET STREET, FOR W. BAYN£S, (SUCCESSOR TO G. TERRY,) 54, PATERNOSTER-ROW : SOLD ALSO BY J. ARCHER, DUBLIN J AND ALL OTHER BOOKSELLERS. 1802. Directions for finding and binding in the Plates, with an Account of their Contents. The Frontifpiece faces its Explanation before the Title Page. PART I. Of Geometrical Lines. PLATES. PAGES, 1. To divide a Line into equal Parts, to divide a Freeze, to raife Perpendiculars, and to illuftrate the Ufe of the SetStor - - b aces Page 28 2. Of Scale of Tenths, Chords, Sines on the Se6lor; to draw an Oval by the Sedlor ; and of various geometrical Figures - - - 32 3. To draw Polygons, Ovals ; and to find the Center of Ovals - - 44 4. To take the Plan of a Room for a Carpet . - _ _ 47 5. Of mitering a Comb-Tray, and Mouldings of different Projeflions ; of Raking Mouldings, and the Tufcan Pediment _ - - _ ^5 6. Various Geometrical Solids, and of finding Curve Lines to anfwer the Sec- tions of irregular figures - - - - 56 7. To find Lines for Hip and Eiiptic Domes - - - 84^ 8. The Tufcan Order _ _ - - - 102 9. The Doric Order _ _ _ - - 109 10. The Ionic Order - - - - -ill 1 1 . The Compofite Order . - - - - 1 14 12. The Corinthian Order - - - - - -116 13. Of diminifliing the Shaft of a Column, and of the Ionic Volute - 113 PART Tl DIRECTIONS FOR P A R T II. Of Perfpedlive. PLATES. 14. The Elementary Planes, and Nature of the Eye '5 16 17 18 19 20 21 22 23 24 25 26 PAGES. Faces Page 182 227 /^ The Reprefentation of Squares in different Pofitions Squares in Inclined Planes _ - - - 234 Ditto Ditto - _ . - - 241 The Reprefentation of Cubes and Prifms -, - - S44 The Reprefentation of Polygonal Figures . _ _ - 357 The Reprefentation of a Row of Equidiftant Columns, and of Long and Short Diftances - - - - - 268 Curvilinear Figures _._---- 289 The Reprefentation of Steps, and the Tufcan Pedeftal and Bafe - 297 The Reprefentation of the Tufcan Entablature, and of Arches - - 302 The Reprefentation of Houfes and Chairs . - _ 309 The Reprefentation of Tables and a Commode - - " 3^5 The Reprefentation of a Cylinder Deflt and Book-cafe, of a Chair oblique, and Shadows in general ; bound in by a Guard - - 329 PART III. Of Pieces of Furniture. 25. The Univerfal Table ..... a6. Sideboard Table ; marked on the Plate 54 by miftake. N. B. The Brafs Rods are made by Mr. Pentou and Co. New-flreet Square, near St. Andrew's Holborn - - - - - - 27. Book-cafe Doors - - - - - . - - 28. A Secretary and Book- cafe .._._- 29. Book-cafe Doors . _ - - - . - 2g. A Sideboard Table .___._ 30 A Library Table, binds in without a Guard ... 356 363 368 37^ 368 363 37« I. A FINDING THE PLATES. PAGES. Vil PLATES. 31. A Sofa, and the Perfpeaive Lines of it; binds in without a Guard Faces Page 379 32. Drawing-Room Chairs . . . _ _ -g» 33. Parlour Ditto - _ _ . _ j^id 34. Drawing and Parlour Ditto - - - _ Jbid 35. A Sofa - - . . . . . ^gg 36. Chair Backs - - _ . , . ,g« 37. A Lady's Writing Table - - _ . . ogg 38. Tripod Fire-Screens - - - - _ -qq 39. Knife-Cafes, and Lady's Travelling-Box - - - aqi 40. Alcove Bed - _ _ _ _ _ _ ,g 41. A Summer Bed - - . . , _ -o_ 42. Corner Bafon-Stands - - - . _ .__ 43. Wartihand Stand, Pot Cupboard, Secretary and Screen Table - 394 44. A Reading and Writing Table - - - _ oq5 45. A French State-Bed - - . ^ _ . g 45. A Lady's Drefling-Table - . ._.-„- 47. A Cylinder Delk and Book-cafe - - - - _ onn 48. A Cabinet - - - - . - - 403 49. A Cabinet and Drefling-Table -.-:;_ .^^ 50. A Lady's Cabinet and Writing-Table - _ - 407 51. Window Curtains and Drapery - - _ _ o 52. A Gentleman's Secretary - - . J' - - - 409 53. A Cylinder Wafhhand Stand - . _ - 411 54. Pembroke Table and French Work-Table - _ . - 412 55. Tripod Candle-Stands . . _ _ - 416 56. A Harlequin Pembroke Table - - - _ j.,* 56. Ornament wK DIRECTIONS, &c. HLATES. PAGES. 56. Ornament for a Freeze or Tablet - - Faces Page 430 57. Pediments for Book-cafes - - ... ^.ji 58. A Kidney Table - - - - - 378 59. Cornices at large - - - - 4,3a 60. The Lady's Drawing Table, and the Dining-Parlour - - 437 61. The Drawing Room , . . - . 444, CONTENTS. ' CONTENTS. Addr.ess Page 5 A Book publirtied before Chippendale's ' 6 Chippendale's next in order of Time ibid. Chippendale's Remark on the Ufefulnefs of Perfpe£live 7 After his there appeared another Book of Defigns in Chairs only. ... ; ibid. An Apology for a Remark made on Chippendale's Third Edition ibid. Ince's and Mayhew's Book of Defigns fucceeds that one of Chairs only ibid. Hepplewhite's Upholfterer's Guide, publifhed in 1788 — Remarks on it 8 The Cabinet-maker's Book of Prices, publifhed in the fame Year — Remarks on it. . ibid. The Stability of the Plan on which the Cabinet Drawing-Book is publifhed 9 Conclufion of the Addrefs lo Remarks on Malton's Criticifms 1 1 PART I. Of Geometry. Introdudion , i^ The term Geometry defined ibid. RegjiJar Geometry not necefTary to Workmen in attaining a competent Knowledge of Lines i5 Geometry founded upon a few Principles of common Senfe ibid. Technical Terms propofed to be explained 17 SECT. I. Of Geometrical Lines. Problem 1. To divide a Right Line into any Number of equal Parts by the firfl Opening of the CompaflTes 10 ■ 2. To divide a Freeze , 21 3. To raife a Perpendicular by different Methods 25 — — — 4, Ditto , ,, ,, ,,, 23 b SECT. li CONTENT S. SECT. II. Of Geometrical Problems. Of the Ufe of the common Cafe of Inftruments Page 24 The Conftruflion and Ufe of a Scale of Feet and Inches — its Derivation ibid. ■■ of a Scale of Tenths 25 ————————— of a Scale of Chords a6 On the Protraftor — its Derivation 27 Of the SeiSlor — its Derivation 28 Of the Line of Polygons on the Sedtor — its Derivation 30 ~^— of Chords on Ditto 32 . of Sines on Ditto 33 Of the Tangent Line on Ditto — its Derivation 35 SECT. III. Of Geometrical Figures. The Names of Geometrical Figures ought to be known 36 Of Superficies — its Derivation 37 Of various Triangles 38 Of Mixtilineal Figures 4'^ Of Polygonal Figures — the Derivation of the Term Pentagon ibid. Tiie Names of the various Sorts of Polygons 41 What the Sedlions of a Cone produces 42 A Circle and an Oval the only regular Surfaces bounded by one Line — the Deriva- tion of the Term Ellipfis ibid. SECT. IV. Of drawing Geometrical Figures. Of drawing various ufeful Geometrical Figures 42 Problem 5. To draw a Geometrical Square 43 . 6. To draw a Rhomb ibid. .. 7. To draw Polygons 44 ■ 8. To defcribe a Hexagon 4.5 9. To defcribe a Heptagon ibid. — — 10. A Circle given to find the Sides of a Pentagon 46 _ • II. The Infcription of a Hexagon ibid. . 12. Different Methods of drawing Ovals 47 13. Ditto ', 48 14. Ditto ihid. — 15. Ditto .,.,... 49 Problem CONTENTS. Hi Problem i6. Different Methods of drawing Ovals Page <o ■ 17. Ditto jj J 18. To find the Center and Diameter of an Oval qa 19. To find the Center of any Segment r^ 20. To find tlie Diameter of a Cylinder without meafuring its Eud 54 S E C T. V. 0/ Geometrical Solids. Oi the Names and Properties of various Geometrical Solids ec Derivation of Hexaedron and Prifm c6 Derivation of Tetrahedron ty The Learned differ about the Derivation of tiie Term Pyramid en Derivation of the Terms Hemifphere and Seaion 61 Of the Se6tions and Coverings of regular and irregular Figures ibid. Problem 21. Of the Covering for a Vale 64 22. Of the Covering of an irregular Vale 66 Of the Covering of a Sphere 67 23. The Sedion and Covering of a Knife-cafe 68 SECT VI, Problems pertaining to the forking Fart. Problem 24. How to cut all the Steps of a Ladder to their proper Length before any Part of it is put together -q 25. How to draw an Elliptic Cornice, and to fit a Valance to it yi 26. To defcribe a Segment of a large Circle without a Center 75 27. To take the Plan of a Room for a Carpet *^ 28. To miter any Thing of the Nature of a Comb-Tray «5 29. To miter the fame when the Sides of the Tray are oblique to each other 78 ■ 30. To find Lines for mitering a Clock Bracket «„ 31. Of mitering Raking Mouldings gg 32. Of mitering Mouldings of different Projeftions gl Of the Tufcan Pediment jj,jj The Nature of Hip and Elliptic Domes g- 33. To conftruft a Hip Dome g^ 34. To con(lru£l an Elliptic Dome gg SECT. VIL 0/ the Proportion of the Five Orders. Introduftion g Of the Origin and Antiquity of the Orders , , . . , . 01 b2 The iv CONTENTS. The Derivation of the Term Architedure Page oi Its Progrefs in building a City and Tower to reach tlie Heavens 92 No regular Proportions affigned to any Pillars before thofe of Jachin and Boaz in Solomon's Temple ibid. Pillars were in ufe long before Solomon's Time ; but no mention is made of their Proportion, except what Jofephus fays of their Height ibid. The Proportions of Jachin and Boaz anfwer to the moft Ancient Doric Order 93 Some Particulars wherein they refemble each other ibid. What Vitruvius fays of the Antiquity of the Doric Order does not confift with other Fa6ls ..., 96 The Ionic next in order — a Temple built of it at Ephefus ibid. The Corinthian fucceeds — Vitruvius's Account of its Origin ibid. Who Vitruvius was ibid. The Tufcan Order the Fourth in point of Antiquity 97 The Compofite the Laft ibid. The Compofite Cnpital derived from the Corinthian, and not limited to one Kind. . ibid. The Chara6lcr and Proportions of the Tufcan Order 98 The Diminution of a Column. . .\ JOO Sir William Chambers's Remarks on Diminution loi The common Method of Diminution ibid. The beft Standard for the Quantity of Diminution 102 Vignola's. Method of Diminution 103 Nicomedes's Inftrument for diminifhing Columns ibid. Of tlie principal Parts of a Column, and the Names of each Member 104 Of the Charafter and Proportions of the Doric Order 109 Of the Chara£ler and Proportions of the Ionic Order. 1 1 1 How to defciibe the Ionic Volute 112 To graduate the Fillet of tlie Volute 113 Of the Charader and Proportions of the Compofite Order 114 The CompoGte Order (hould be placed before the Corinthian — Reafons why, fhewn ibid. General Proportions of the Compofite Order 115 Of the Charadler and Proportions of the Corinthian Order 116 How to draw the Scatia, Cymaredla, and Cymainverfa ; . 118 Obfervations on the Agreement of the Five Orders ibid. Of the Proportions of Frontifpieccs 1 20 General Diredions for drawing the Five Orders — Indian Ink J 2 1 PART CONTENTS. > PART II. Of Perfpeclhe. Introdudion Page 177 SECT. I. Principles of Perfpedive, Of the Principles on which Perfpedlive is founded 182 Of the Elementary Planes 188 The Ground Plane 189 The PerfpecSlive Plane ibid. How the Appearance of Objedts may be determined on Glafs 190 The Horizontal Plane ipr The Direiling Plane 196 The Vertical Plane ibid. The Vifual Plane 198 Of Lines produced by the Interfedlions of the foregoing Planes 200 Of Points produced by the Interfedtions of thefe Lines 202 S E C T. II. Of Optical Laws. Of the Affinity of Opticil Laws with the Principles of Perfpeflive 205 The Ufe of the thrte principal Elementary Planes in the Pradtice of Drawing 211 Of various Pofitions of Lines to the Pidlure 315 How a Geometrical Square appears on tlie Plane of the Pidlure in various Cafes. ... 217 SECT. III. Of Problems in Perfpeaive. Problems folved according to the preceding Principles 22C The ufual Metliod of teaching Perfpedlivc is to begin with Points and Lines ibid. Thefe unnccefTary, becaufe included in finding the Rcprefentations of Superficies. . . 226 Problem i. To reprefent a Square lying on the Ground , 227 2. perpendicular to the Ground and to thePidture 228 3. perpendicular to the Ground and parallel to the Pidlure 230 4- inclined to the Ground, and perpendicular to the Pidture 23 1 ' — 5- inclined to the Ground and to the Pidlure. . . . 234 6. To find the Reprefentation of a Square lying on the Ground, having its Sides oblique to the Pidture 236 ' 7- To find the Reprefentation of a Square perpendicular to the Ground and oblique to the Pidture 238 7 Problem *i CONTENTS. Problem 8. To find the Reprefentation of a Square, having its Sides oblique to tlie Piifture, and fituated in a Plane inclined to the Ground. . . . Page 239 ■ 9. To find the Reprefentation of a Square fituated in a Plane oblique both to the Ground anJ to the Pidlurc 241 ■ 10. To reprefent a Floor of Squares 244 1 1 . To reprefent a Row of Cubes parallel to the Pitlure 246 ' 1 2. To reprefent Cubes oblique to the Picture 248 13. To reprefent objedts when the Diftance and Vanifliing Points exceed the Bounds of the Pi(£lure 250 ' 14. To reduce the Point of Diftance to the Limits of the Pi61ure 254 SECT. IV. The Reprefention of Obje£is. Of the Reprefentation of Polygonal and Curvilinear Figures 257 Remarks on Polygons ibid- Problem 15. To reprefent a Hexagon having two of its Sides parallel to the Pifture 259 16. To find the Reprefentation of an Hexangular Prifm 260 I 17. To find the Reprefentation of an OiSagon, having two Sides parallel to the Pi(£lurc 262 ■ 18. To find the Reprefentation of an Odtangular Prifm, having its Sides oblique to the Picture 263 Remarks on the Difference between the Reprefentation of Objefts on a Plane, and their Appearance to the Eye 265 Of the Reprefentation of a Range of Equidiftant Columns 269 Of the proper Choice of the Diftance of the Pidture, proportioned to the Heiglit of the Horizon 275 How to choofe a Diftance when the whole Length of the Pifture is filled with Ob- jcds on the Front 2S0 How to choofe a Diftance when the Objefts are drawn by a large Scale, fituated not far from the Center of the Piflure 281 How to choofe a Diftance when a Piece of Furniture, not very long, is reprcfcnted near the Middle of the Front of the Pidure. 282 Of the Reprefentation of Curvilinear Figures 283 Problem 19. To reprefent a Circle lying on the Ground Plane 289 20. To reprefent a Circle perpendicular to the Ground and to the Picture. . 291 21. To reprefent a Cylinder eredl on the Ground 292 — — 21. To reprefent a Cylinder lying on the Ground and oblique to the Piflure 293 Problem CONTENTS. yii Problem 33. To find the Reprefentation of a Semi-ellipfis whofe tranfverfe Diameter is parallel to the Pidure Page 204 . 24. To find tlie Reprefentation of an Elliptic Segment inverfely jgc SECT. V. Application of the Problems. The Application of the preceding Problems to the Pradice of drawing Pieces of Ar- chite(5ture and Furniture jqg Example i . How to reprefent a receding and returning Flight of Steps 297 2. How to reprefent a Tufcan Bafe and Pcdeftal 299 3. How to reprefent a Tufcan Entablature and Bafe 302 4. How to reprefent Arches -07 s- Ditto ......'!..!!!!! 308 5. How to reprefent a Houfe having its Front Parallel to the Pidure 309 7. To find the Reprefentation of a Houfe when the Gable-end is parallel to the Pidure - j j 8. How to reprefent a Chair when its Front is parallel to the Pidure 31a 9. How to reprefent a Chair when its Front is perpendicular to the Pidure 314 ■ 10. How to reprefent a round Pillar and Claw Table 31^ — ^— II. How to reprefent an odagon Ditto ,iQ 12. To put a Commode in Perfpedive when its Front is parallel to the Pidure 317 13. To reprefent a Chair when its Front is oblique to the Pidure 319 14. To put a Cylinder Delk and Book-cafe in Perfpedive when its Front is oblique to the Pidure 021 SECT. VI. The Principles of Shadows. A fhort View of the Nature and Principles of Shadows 035 Preparatory Obfervations Hjjj Cafe I. To projed the Shadows of Objeds in various Pofitions when the Sun's Rays are parallel to the Pidure ^28 Example i. Ditto -^ 2- I^'"° .'.'.".'.'.'.".' 330 3- Ditto ibi,,, 4- Ditto 22J Example i. When one Objed Aands in the Way of the Shadow of another 332 2. Ditto ibid. Cafe 2. To projed the Shadows of Objeds when the Rays come in a Diredion from behind the Pidure „„. Obfervations on the Theory of Cafe 2 355 Cafe viK CONTENT S. Cafe 3. To find the Projeftion of Shadows when the Sun's Rays come on the Front of the Pidure Page 340 Example i. When the Shadow falls on the Ground ibid. — ^^— 2. When the Shadow falls on upright, oblique, and horizontal Planes 341 Of Shadows when the Sun does not {hine 343 Of the Proportion of Tints in a Pidlure 345 Of rcfleded Images on Water 347 TO THE BINDER. The above are the General Contents of the Firfb and Second Parts, to be bound up at the beginning of the Work. — The Index, containing an Account of the Third and Fourth Parts, to be bound up at the End of the Work. •• TO CABINET-MAKERS AND UPHOLSTERERS IN GENERAL. GENTLEMEN, I PRESUME, that to publlfli a Drawing-book anfwerable to the preceding title page will not require many words to convince you either of the neceffity or propriety of the attempt. Nor will it be requifite to ufe an oftentatious preface to recommend it to your notice, or to perfuade you of the utility of fuch an undertaking. There- fore, what I have further to fay in this Addrefs (hall be to give fome account of my plan, and point out to you the difference between this and other books which have been publifhed for the affiftance and ufe of Cabinet-makers and Upholfterers. Books of various defigns in cabinet work, ornamented according to the tafteof the times in which they were publifhed, have already appeared. But none of thefe, as far as I know, profefs to give any inftrudions relative to the art of making perfpedive drawings, or to treat of fuch geometrical lines as ought to be known by perfons of both profeflions, efpecially fuch jof them as have ( 6 ) have a number of men under their diredions. Nor have thefe books given accurate patterns at large for ornaments to enrich and embeUifh the various pieces of work which frequently occur in the cabinet branch. Such patterns are alio highly neceflary to copy from by thole who would fufficiently qualify thcmfelves for giving a good fketch, or regular drawing, of any thing they meet with, or are required to draw for others. Nor indeed would this per- formance anfwcr fo well to the title of a Drawing- book without them. I hope, therefore, that in fome degree the above defedl is fuppUed in the follow- ing work, and that it will be confidered as an enhancement to the real value and ufefulnefs of the Cabinet-maker and Upholfterer's Drawing-Book to be furniflied with a variety of fuch ornaments as fhall ferve, both for the pur- pofe of the learner, and alfo to affifl the ideas of thofe who have occafion to adorn their work in this way. As I have alluded to fome books of defigns, it may be proper here juft to fay fomething of them. I have feen one which feems to have been publifhed before Chippendale's. I infer this from the antique appearance of the furni- ture, for there is no date to it ; but the title informs us that it was compofed by a Society of Cabinet-makers in London. It gives no inftrudions for draw- ing in any form, but we may venture to fay, that thofe who drew the defigns wanted a good fhare of teaching themfelves. Chippendale's book feems to be next in order to this, but the former is without comparifon to it, either as to fize or real merit. Chippendale's book, has, it is true, given us the proportions of the Five Orders, and lines for two or three cafes, which is all it pretends to relative to rules for drawing : and, as for the defigns themfelves, they are now wholly antiquated and laid afide, though pofTefled of great merit, according to the times in which they were executed. But it may here be remarked to his credit, that although he has not given rules for drawing in * perfpedive himfelf, yet he was fenfible of their * This is ftri(ftly true of the third edition of Chippendale's book ; but the firft edition of it, printed in 1754, has given two chairs, a dreffing-table, and a book-cafe in perfpedlive, fhewing the lines for drawing them. But why thefe examples were not continued in the fucceeding editions I know not. In ( 7 ) . their importance and ufe hi defigning, and therefore he fays in his preface : ** Without fome knowledge of the rules of perfpedlive, the cabinet-maker cannot make the defigns of his work inteUigible, nor flievv, in a little com- pafs, the whole condu6t and efFe£l of the piece. Thefe, therefore, referring to architedure alfo, ought to be carefully fludied by every one who would excel in this branch, fince they are the very foul and bafis of his art J' . After Chippendale's work there appeared, in the year fixty-five, a book of defigns for chairs only, though it is called " The Cabinet-maker's real Friend and Companion," as well as the Chair-maker's. This publication profefles to fhew the method of ftriking out all kinds of bevel-work, by which, as the author fays, the moft ignorant perfon will be immediately acquainted with what many artifts have ferved feven years to know. But this aflertion both exceeds the bounds of modefty and truth, fince there is nothing in his diredlions for bevel-work, which he parades fo much about, but what an ap- prentice boy may be taught by feven hours proper inftrutflions. With refpe(£l to the geometrical view of the Five Orders which he has given, thefe are ufeful, and the only thing in his book which at this day is worthy notice; as all his chairs are nearly as old as Chippendale's, and feem to be copied from them. The fucceedlng publication to this feems to be Ince's and Mayhew's Book of Defigns in Cabinet and Chair work, with three plates, containing fome examples of foliage ornaments, intended for the young defigner to copy from, but which can be of no fervice to any learner now, as they are fuch kind of ornaments as are wholly laid afide in the cabinet branch, according to the pre- fent tafte. The defigns in cabinets and chairs are, of courfe, of the fame caft, and therefore have fuffered the fame fate : yet, in juftice to the work, it may be faid to have been a book of merit in its day, though much inferior to Chippendale's, which was a real original, as well as more extenfive and maf- terly in its defigns. In the laft edition of any work, wc naturally expeft to fee it in its beft fiate, having received its laft revifal from the author, or fome other hand equal to the tafk ; and therefore it can never be thought unfair for a reader to form his judgment of a book from the laft impreflion. I hope, therefore, this will fufficiently apologize for the above obli^rvation. 4 In ( 8 ) III looking over luce's book I obferved two card-tables with fome perfpec- tive lines, fhewing the manner of defigning them. Thefe, fo far as they go, are a ufeful attempt ; but certain it is to me, from fome experience in teach- ing, that no perfon can have the fmallefl acquaintance with the principles of perfpcctive, merely from feeing two or three lines joined to a plate, without proper inftrudlions by letter-prefs. It is true, a defcription is given of thefe lines in the 7th page of his book, but not equal to what is abfolutely requiiite to fuch as have no previous acquaintance with the art j and thole that have, will not require that which can give them no affiftance. Properly fpeaking then, what is done in this book, relative to perfpcdive lines, can only lerve as a hint to the workman, that this art is eflential in defigning. In the year 1788 was publifhed, *' The Cabinet-maker's and Upholfterer's Guide." In which are found no diredions for drawing in any form, nor any pretenfions toit. The whole merit of the performance refts on the defigns, with a (hort defcription to each plate prefixed. Some of thefe defigns are not without merit, though it is evident that the perfpedlive is, in fome inftances, erroneous. But, notwithflanding the late date of Heppclwhite's book, if we compare fome of the defigns, particularly the chairs, with the neweft tafte, we fhall find that this work has already caught the decline, and perhaps, in a little time, will fuddenly die in the diforder. This inftance may ferve to con- vince us of that fate which all books of the fame kind will ever be fubjed to. Yet it muft be owned, that books of this fort have their ufefulnefs for a time ; and, when through change of fafliions they are become obfolete, they ferve to fliew the tafte of former ages. I fhall now conclude this account of books of defigns with obferving, that in the fame year was given a quarto book of different pieces of furniture, with the Cabinet-maker's London Book of Prices j and, confidering that it did not make its appearance under the title of a Book of Defigns, but only to illuflirate the prices, it certainly lays claim to merit, and does honour to the publifliers. Upon the whole, then, if tht intended publication, which now petitions your patronage and fupport, be fo compiled and compofed as fully to anfwer, and ( 9 ) and alfo to merit, t?ie title which has been given to it, I think it will be found greatly to fupply the defefts of thofe books now mentioned, and will appear to be on as lafting a foundation as can well be expefted in a work of this kind. For inftance, the firft part, which provides the workman with geometrical lines, applied to various purpofes in the cabinet branch, cannot be fubjeft to alteration any more than the principles of reafon itfelf. The fame may be faid of Perfpedive ; the fubje6l of the fecond part. This art, being founded on Geometry and Optics, may be improved in its pradice, but its fundamental principles can never be altered, any more than the nature of vilion itfelf. As to the defigns in furniture contained in part third, thefe are indeed liable to change; nor is it in the power of any man to provide againfl: it, by making fuch drawings as will always be thought new. Yet the inftruclions given on the manufaduring part being founded on real experience and practice, will be much the fame at all times. It alfo adds to the ufefulnefs of the de- figns, that I have in general given their geometrical dimenfions, either laid down on the ground, or other fcale lines adapted for that purpofe, or elfe de- fcribed them in the letter prefs. So that no perfon, however ignorant of per- fpe6live, can eafily miflake the perfpe6live for the geometrical meafurements, or be at any lofs to know the general fizes of fuch pieces as Ihall be intro- duced. In proceeding, however, with the firft edition, I found that to give fcales for the perfpedive heights and widths could not be done, in many inftances, without encumbering the defigns in fuch a way as greatly to hurt their appear- ance. To remove this inconvenience, and to aflift thofe who have a little knowledge of perfpedive, in obtaining the true meafurements of fuch defigns or engiavings as may have no fcales to them, I have flievvn, in the perfpedive part, that this may be eafily done, by finding the vanifiiing points and diftance, and tracing their vifuals forward to the ground line. In the firft edition this is done at the end of the Appendix, becaufe its ufefulnefs did not ftrike me till I came to that part of the work. With refped to mouldings and various ornaments, the fubject of the fourth part, it is granted that thefe are of a changeable kind. Yet it is pretty evident B that ( 10 ) that materials for proper ornaments are now brought to fuch perfe«5lion as will not, in future, admit of much, if any, degree of improvement, though they may, by the (kill and touch of the ingenious hand, be varied, ad infinitum^ to fuit any tafte at any time. Lafllv, I would intreat leave gratefully to acknowledge the general encou- ragement I have been favoured with in going through the firft edition : and though my vaft expence has deprived me of the emolument that might have been expe(5led from fo numerous a fubfcription, yet it is fome confolation to be confcious that I have fpared no expence, nor withheld any thing in my power to do the work juftice, and give fatisfadtion to the public. And I have the additional happinefs to know, from feveral teftimonies, the full approbation that the work has obtained in the judgment of the candid and Ikilful. And, notwithftanding the ill nature of fome, who hate to fpeak well of any thing but their own productions, I only wifh that a comparifon be made with any other book hitherto publifhed for the ufe of Cabinet-makers and Up- holfterers, and then it will fufficienly fpeak for itfelf. And now, in going through this fecond edition, it is ftill my fteady interim tion to contribute as much as I can towards improving the work, and render- ing it as complete as is in the power of,. 6ENTLEMEN, Your humble Servant,. THOMAS SHERATON.. TO II TO THE READER. Near the conclufion of the flrft edition I had put into my hands a work, written by Mr. Malton, entitled the New Royal Road to Geometry ; at the end of which there is an Addenda and Poftfcript to the reader, containing fome ftridures on a fmall piece written on perfpedive by Mr. Bradberry, whom he pofitively accufes of having copied, verbatim, Mr. Martin's fmall performance on that fubje£l. I have read Mr. Martin's, but not Mr Brad- berry's, and therefore whether this charge be juft, I am not a competent judge; but if, as Mr. Malton affirms, the latter is nearly a literal copy of the former, then, in a fenfe, I may be faid to have alfo read Mr. Bradberry's. But if in Mr. Bradberry's performance there are any errors, the blame muft originate with Mr. Martin, of which it feems Mr. Bradberry's is a faithful copy, for Mr. Malton fays, " The whole of the letter, and the diagrams alfo, being exa(5tly copied, without the lead variation or tranfpofition ; no varying the expreflions to give an appearance of being his own ; the very re- ferences are by the fame letters, and every, even the moft palpable error, truly and faithfully copied." See Poftfcript, p. 26. So it appears that the ingenious Mr. Martin was capable of grofs errors in perfpeftive with all his mathematical fkill. Yet Mr. Malton, in his critique on the various authors that have written on this fubjecl, did not think it worth his while fcarcely to notice it; for he fays, " He thought it fo infignificant a work as to deferve not four lines to be faid on it." Grofs errors, then, accord- ing to this gentleman, deferve no attention when they appear in fmall pietes, not even when their authors are of great repute. An Emerfon, a Muller, an Ozanam, a Prieftley, a Fergufon, or a Martin, are as nothing, and lefs than nothing, in his eftimation. What a wonder it is then, that poor Bradberry is in the leafl: noticed by this greateft of champions in perfpedtive, fincc he is convinced that this wonderful man, as he calls Bradberry, knew nothing at all of perfpeiftive. On confidering, therefore, how little thefe B 2 names ( '2 ) names of repute appear in the eyes of Mr. Malton, I cannot but congratulate myfelf in conning ofFfo moderately under the lafh of him whofe vigilant hand of chaftifement none have efcaped, lefs or more. Our author begins his remarks in the following manner : " A quarto work has been publifhed fuice the commencement of the year 1793, by a Mr. Sheraton, Cabinet-maker*, called, The Cabinet-maker and Upholflerer's Drawing-Book, which feems to intimate its being of no ufe to any other." It intimates that it is chiefly intended for their ufe, though not to the ex- clufion of any other who are concerned to know perfpeftive. And, what- ever Mr. Malton may think, we have rcafon to believe, and have had fome proof from trial, that any mechanic, whether cabinet-maker, carpenter, or any othep that requires a general knowledge of perfpeftive, will fooner obtain it in the Cabinet-maker's Drawinsr-Book than in Mr. Malton's moft; elaborate performance ; we mean not to fay that the former is fo worthy the attention of mathematicians as the latter; far from It. And though, as our remarker obferves, " A large part of the book is on perfpedlive applied to furniture, and that without any pretenfions to improve, or render the fubjedl more clear ; yet we believe, from teftimonies written to the author, and other perfonal remarks, that fome Iktie portion has been contributed, in the Cabinet-maker and Upholllerer's Drawing-Book, towards rendering the fubjeft more intel- ligible to workmen than has hitherto been done in any other work. And the author thought it more modefl: to avoid any pretenfions to improvement until he found what was the opinion of others, after having finiflied the whole. It is too common to hear of propofed improvements, and new lights on fubjefls, which after all turn out in the end to be none at all." In the next breath our author fhews his wonted contemptuous fpirit on all who write on his favourite fubjedl:. " I fhould have taken no notice of this produdtion, had not the author given fome glaring proofs of his incompetency in perfpedlive." * Mr. Malton, who is certainly one of the firfl writers on perfpecSlive, Was himfelf a Cabinet- maker; and to this, as a brother craftfman, perhaps it is owing that I am fo moderately dealt with. And ( ^3 ) And here the candid reader will pleafe to obferve, that this great outcry of incompetency with which we are charged, amounts to no more than a matter of mere fpeculation, which by no means aftedts the practice of perfpedive, and which Mr. Malton himielf, in the next page, calls a fmall miftike; for though he here refers to the oblique fedion of a cone, which he lays proJuces an ellipfis of equal curvature at each end, it is clofely conneded with the other point on which the charge of incompetency is founded; namely, that the per- fpedlive reprefentation of a circle feen obliquely, is an irregular ellipfis, which Mr. Malton affirms to be regular. Now, whichever way it be, rules to the fame efFe6l for putting a circle in perfpective are propofed by both; for if his rules produce a regular ellipfis, Co do mine; as the reader may fee by com- paring each together. To convert then a fmall miftake into a glaring proof of incompetency, is, in my opinion, taking the advantage, and is a glaring proof of a want of candour. It is, however, but juftice to remark the candour which appears in the fol- lowing paflage: " Probably," fays Mr. Malton, " the feveral writers on the conic fedions have not well confidered this matter; future writers would do well to confider it, and benefit themfelves of this author's obfervations there- on. Or that Mr. Sheraton reconfiders (fhould it not be reconfider) it with at- tention, before he publiflies a fecond edition ; and if he fliould find himfelf luidcr a fmall miftake, that he will not be afhamed to acknowledge it can- didly ; it would redound more to his credit than to perfift (is there any occa- fion for, and perfevere) in error, though it may not appear quite clear to him ; but, as acquiefcing in the general concurrence of fo many fcientific men of greater repute in the world of fcience." To this it is anfwered, that we cannot but comply with fo juft arequifition as to re-examine the fubje6l, and even to fubmit to the general concurrence of fcientific men, if after all it remain a doubt to us ; and fliould the refult of future inquiries on this fubjed prove decifive in favour of Mr. Malton, the error will be frankly acknowledged. Mr. Malton next obferves, *' that there are fome few inaccuracies in this work," which mufl mean the whole work ; and therefore it is no fmall fatif- fadion to me, to find, after the revifal of fo able a hand as Mr. Malton, that the inaccuracies are but feWj and that thefe particularly lie hi the rakin I mouldings ( 14 ) mouldings for pediments, which, in fa£l, take up little more than half a quarto plate. But though thefe, according to our author, are particularly the things where the inaccuracies are found, yet he does not point out to the reader what thefe are in any infrance. His next remark is, " that in Plate XVII. Fig. 1 1, there are fome unne- ceflary lines, in order to determine the vanifliing line of a plane inclined ob- liquely to both the horizon and the picture." But Mr. Malton ought to have confidered, that in Fig. ii. are two methods of determining the vanifliing line of a plane inclined both to the horizon and pidlure. And, befides, he certainly knows that I have there (hewn the vanifliing line in two different degrees of obliquity to the horizon, one at an angle of 28 degrees, the other at 45 degrees, which accounts for fo great a concurrence of lines. And, moreover, before he had pafled this cenfure, he ought in juftice to have examined page 241, in M'hich a reafonable apology is made for the intricate appearance of thefe lines. But if the reader is merely to judge of unnecefTary lines by their great number interfering each other, let him look into Mr. Malton's own performance, and then let him fay whether, in condemning others for this fault, Mr. Malton has not involved himfelf in the fame cenfure. The next obje£t of his criticifm is an inclined pofl: in Plate XXVI. or the laft in perfpe6live, whofe reflefted image he apprehends fliould be meafured from the furface of the water, becaufe of the ground's variablenefs. In this Mr. Malton differs from fome other writers of repute, who meafure from the bafe of the objefl:, not from the furface of the water. Mr. Kirby, forinftance, meafures from the ground, Plate XVI. Fig. 4. as alfo Dr. Prieftley. This nice point, however, we iTiall reconfider in its proper place. In refpea to the Problem in page 71,1 acknowledge it is not fo geometri- cally flated as it ought to be ; but the ufe and application of it is ftill the fame to workmen, being intended to Ihew how the fteps of a ladder, whofe fides are inclined to each other, may be cut to their proper length without firft putting any part of it together. INTRO- INTRODUCTION T O PART THE FIRST. Geometry literally means, to meafure the earth *, but in praftice is applied to many arts and trades, as well as fcience in general. With refpedl to that part of it which becomes ufeful to us, it is pleafant and eafy, readily under- ftood, and of a mechanical nature ; fo that no workman need to be fliocked or frightened at the idea of learning fuch geometrical lines and figures as (hall be confidered in the fubfequent pages. Nor is it requifite to the workman to * Geometry ; from yij gi, the earth ; and i^sr^ov metron, to meafure. It appears from general hif- tory, that the Egyptians were the firft who apphed this art to meafuring the earth. The river Nile, wliich overflowed its banks, fwept away thofe boundaries, or land-marks, which ferved to diftinguifh their different eftates. This made it ncceflary for them to take plans and draughts of their fields, to afcertain their quantity, and know their proper fituation. To obtain accuracy in thefe, prompted the ftudy and improvement of Geometry in that nation ; but various other reafons fince have induced men to cultivate this fcience. Some have contended that the Hebrews were the firfl inventors of it. Jofephus is of this opinion ; and fo far as the invention of flringed inftruments of mufic, the working of brafs and iron, and the building of the city of Enoch, required the aid of geometry, it mufl be ac- knowledged that the Hebrews, Jubal and Tubal-cain, were the inventors of it, and that at a period long before Egypt exifled as a nation. Thefe perlbns, living the length of five or fix of tlie lives of men in after ages, might probably bring this fcience to a greater perfedlion than we are apt to imagine; and as Egypt appears to be the fecond nation in point of antiquity, originally flyled in Scripture the Land of Ham, I think it rational to fuppofe that the Egyptians had firft derived their ideas of geome- try from the Hebrews, but that the Egyptians were the firft that applied it to the ait of plotting and drawing. begin ( ^^ ) begin with the ufoal definitions in geometry, as thefc would be foreign to my plan, and unneccflluy for him to know. For inftance, he need not be told that a point is without parts or naagnitude, that a hue is length without breadth, or that the terms of a line are points, &c. Sec. Thefc, and a number of others of this kind, are known by the common undcrftanding of every one. I (hall therefore confine myfelf to fMch particulars as every candid workman will at once pronounce ufeful, and which may be applied to the praftice of fome parts of the ingenious art of Cabinet-making. Yet, from what I have here advanced with refped to geometrical definitions, I would not be under- ilood as fpeaking difrcfped^fully of them, much lels to deny their ufefulnefs to Inch as learn geometry regularly. It is impofllble to proceed without thefc, when this ancient fcicnccis taught as the ground-work of mathematical learn- ing. We might as well attempt to teach logic without a method of arrang- ing or diftinguifhing ideas, or arithmetic without the powers and properties of numbers, as geometry diveflied of its chain of definitions and axioms, Sec. by which at length we arrive to the certain knowledge of truth, and are able to demonftrate it to others. But, on the other hand, as it is pofilble for a man of found fenfe to reafon well without knowing the rules of logic as they are taught in fine and regular fyftems, fo I apprehend it is alfo pofllble for a workman of no learning, but what is common, to attain to a ufeful know- ledge of geometrical lines, without the trouble of going through a regular courfe of Euclid's definitions and demonftrations, &c. And we may jufily lay of his definitions and demonftrations, the found of which fo often alarm- ing the ears of the ignorant, that they are, as a certain writer obferves, " l-Aiilt upon a few principles of common fenfe, without which the moft do- meftic and fimple negociations of life cannot be tranfaded ; and that, what they fhun as fubjedls too fublime and intricate for their comprehenfion, are only the moft familiar truths made artificial by regularity, and difguifed by a technical language." Upon this view of Geometry, I fhall now proceed to the confideration of fuch Problems as every workman of tolerable capacity will eafily underfiand, and find advantageous to him. And, ( '7 ) And, for the fake of making every part of this book as intelligible and ufeful as I am able, I fhall, in the courfe of proceeding, explain fuch * technical terms as may be neceflarily ufed in the fubfeqiient pages, and which, for propriety's and brevity's fake, cannot well be avoided on fubjcifis of this nature. And, in attempting this, 1 hope not to incur the difagrecable title of a pedant ; as I pretend not to give thefe explanations as the produce of my own Ikill in ety- mology, but fhall recommend them to the reader as they are found in the writings of men of unqueftionable abilities in this way -f . Befides, when it is confidered that the following work is not written for the learned, but fuch as may want fome afliftance in the derivation of particular words ufed in Geo- metry, Architeflure, and Perfpedive, in order to fix their real meaning more laflingly on their memory, it is prefumcd that this confideration alone will, in the view of the candid, fufficiently apologize for me. As for thofe of an oppofite cafl of mind, it is not eafy to fay what would pleafe, or what dif- pleafe, them. * From fi'xj^yi, techne, art ; which belong to the terms and rules of arts and fciences. t As Chambers, Johnfon, Bailey, Parkliurft, Lemon, &c. THE THE CABINET-MAKER AND UPHOLSTERER'S DRAWING-BOOK. PART I. CONTAINING NECESSARY INSTRUCTIONS FOR OBTAINING THE KNOW- LEDGE OF SUCH LINES AS ARE USED IN BOTH BRANCHES. SECT. I. On dividing a Line into any Number of equal Parts — raifing a Perpendicular on a given Point — and the Method of dividing a Frieze or Pilajler into Flutes and Fillets. * Problem I. Plate I. Fig. i. A RIGHT line being given, to divide it into any number of equal parts. The line to be divided is 7.1, which is to be divided into 7 parts. Operation. — Firft, from 7, on the given line, draw a right line at pleafure, as 7,8, making any angle with the line 7.1 to be divided. Then with the * Problem, '7tpo^>.riii.Xy problema, " from ^clKKui, hallo, to throw; and itpo, before; i. e. to propofe, or fet before : a propofition relating to praftice, or which propofes fomething to be done; as to bifeft a line given, to draw a circle through any three points;" or, as in the prefent cafe, to divide a line into any number of equal parts. C z foot ( 20 ) foot of your compafles fixed on 7, turn the arch* 1.8, and, without any alteration of the inftrument, place its foot in i, and turn the arch 7.9 at pleafure. Second, Take the fpace 1.8, and place it on the arch 7.9 which was drawn indefinitely -|-. Then from i to 9 draw a right line, which will be parallel to the line 7.8. Thus far it fliould be obferved, that the problem teaches to draw two lines parallel, both with difpatch and accuracy. Laftly, with your compafles opened at random, lay on the divifions 1,2,3, 4, 5, 6, on both lines, firfl: from i to 9, then from 7 lo 8 ; and by drawing lines from each correfpondent point, the given line 1.7 will then be divided as required. Obferve, that whatever number the given line is to be divided into, the lines 1.9 and 7.8 are to be divided into one le(s. A little reflexion will point out the reafon of this, if we confider that the lines 7.8, 1.9, are perfe£lly parallel to each other. For if the divifions laid on each line be greater or lefs than thofe fought for, yet lines drawn acrofs to each refpcclive divifion will cut the line to be divided in the fame points ; becaufe what is loft or gained on one line by thefe uncer- tain divifions, will be regained or loft when the fame uncertain divifions are placed the contrarv way on the other parallel line. Tliis is clearly exemplified in the fic^ure by the fmall dotted lines drawn from fmaller divifions, as at 0, which interfea the given hne 1.7 as before. This may be performed by fewer lines, thus: — Let a b. No. 2, be the line to be divided, fuppofe into four; draw ac, making any angle with ab at dif- cr(.t;on, and oi any length. Open the compafles at random, and fpom a to- * Arch, from axus, a bow, Lat. and whea ufed in Geometry implies " any part of a circum- fennce of a circle." t That is, without bounds or limits. wards ( 21 ) wards c lay on four divifions ; draw a line from c to b, and to the line c, b^ e^ draw the line 2, 3, 4, each of them parallel, then will the given line a^ be divided as required. Problem II. Fig. 2. To divide a frieze or pilafter, &c. &c. into any given number of flutes and fillets : I. Let AB be the fuppofed width of the pilafter required to be fluted. Operation. — Draw the right line CD indefinitely. Take then two pair of compafles, one for the flutes, and the other for the fillets ; and with the firft opening of your compafles for the flutes, lay it on C D, and divide this uncer- tain opening ab into three. Again, take one of thefe three parts for each fillet, as c a, and repeat it on the line C D, firfl: a fillet, then a flute, till you have the propofed number, which in this cafe is 5, (and always in pilafl:er3 fliould be an odd number*). Second, Extend your compafl'es from c to d^ the whole fpace which the uncertain divifions include; and with one foot on c or ^/, turn the arches Ec and Ed', and from the point where thefe two arches interfed, as at E, draw right lines to c and d, which will then form an equilateral triangle. Laflly, Draw lines from all the divifions on C D to E. After which, take A B, the given width of the pilaflier, in the compafles, and turn the arch e d, and through the two fedlions ^</ draw a right line, then will ^^beequ.il A B, and the pilafl:er or frieze will be divided in the mofl: accurate manner as required. * Obferve, aiiv opening of one pair of compafles will do the wlioie bufiiiefs, if a previous calcu- lation be made of the equal parts contained in all the flutes and fillets. Thus, in the prefcnt cafe, \vc fay there are five flutes, allowing the fpace of three fillets to a flute, which make together fifteen ; and the addition of fix, the number of fillets in the pilafter, make twenty-one. Therefore lay on t!»e compafles at random twenty-one times, and proceed as above, Problem ( 22 ) Problem III. Fio. 3. To raife a perpendicular from any given point on a line as its bafe. Operation. — Let G be the given point on the bafe line G V. Take then the * radius G O, or any other at pleafure, and turn the arch O S. Fix again your compafs foot in O, and, without any alteration, interfedl the arch at P. On P, with the fame opening of the compafles, make another feftion at S, and from thofe points SP turn an arch each way, and their interfeclion at R will form a point perpendicular with the given point G, as required. This may alfo be effe(5ted another way with more difpatch, but perhaps not always with equal accuracy. Operation. — Let A P, Pig. 15, Plates, be the bafe, and P the point whence you would ereft a perpendicular. With any opening of the compaffes, and with one of its legs fixed any where out of the line, as at R, defcribe the arch O, P, R, till it cut the bafe line, as at O. Then from O draw O R through the center S, cutting the arch at R, and their fedtion will form a point perpendicular to P, as required. Thefe problems may be very ufeful to an Upholflierer when he is laying down the plan of a room for a carpet, as it is not convenient always to take a fquare with him. Befides, by a good line, bradaul, and chalk, a perpendi- cular may be raifed with more exadtnefs than can be drawn on a floor by a fquare. But, as I intend giving fome direflions to the Upholfterer how to lay down a room in an accurate manner, fo that a carpet may be properly cut by his plan, Lfliall at prefent fay nothing more on this fubjeift. * Radius, a right line drawn from the center of a circle to its circumference. This right line, I conceive, anfwers to the rays of light (in optical fenfe), which, falling upon the eye every where in right-lined direftions, form a lioriion to our fight. Problem ( 23 ) Problem IV. Fig. 4. To draw a perpendicular line by a fcale of equal parts, as by a conimon rule, or by a rod divided. Operation. — Let the line G V be the line required to raife a perpendicular from. Let V be the propofed point, and from any fcale of equal parts lay down ten of thofe parts from the point V towards G. Take then fix of thofe parts (or fix inches of the common rule) and turn the arch 1.2 at pleafure. Again, take ten parts, or ten inches of your rule, and place the end of the rule or rod on the eighth of thofe ten parts or inches, as at Q, and with the other hand, by a pencil, interfed the arch 1.2, by which a point will be gained exailly perpendicular to V, as required. This problem will be of ufe to the Cabinet-maker and Upholfterer when neither fquare or compaflTes are at hand. For inftance, if a Cabinet-maker would cut a board acrofs perfeflly fquare, without compafles, chalk line, or fquare, if he have but a rod, let him proceed thus: Divide the rod into ten equal parts, and by this ftraight rod ftrike a line on the fide of the board ; and then lay down ten parts on this line, and proceed as above. SECTION ( «4 ) SECTION ir. On the life of a Common Cafe of Injlruments, together with fame Geometrical Problems confidcred. As the various inftruments found in common cafes are not commonly un- derftood by Cabinet-makers and Upholfterers, and as the principles by which they are devifed and con(lru£ted are purely geometrical, I think it neceffary and ufeful to give an explanation of them, fo far as they can any way aflift the above perfons, or others, in the pradlce of drawing. The firft thinsc that needs be noticed is a fcale of feet and inches. The intention and ufe of a fcale is to reduce the real meafurements of any objedt to a convenient proportion, fo that it may be reprefented on a (heet of paper, &c. with as much exadtnefs as if it were drawn at full fize *. A fcale of feet and inches fliould be ufed when we reprefent any piece of furniture either geometrically or perfpedivcly, becaufe fuch a fcale anfwers to our common rules ; but mathematicians ufe a fcale of tenths. On the ConfiruSlion and Ufe of a Scale of Feet and Inches. To conftru6t a fcale of feet and inches, draw feven lines parallel to each other, and at equal diftances, as in Plate I. Fig. 9. Then, as on the line 1,2,3, lay down as many divifions for feet as will comprehend the largeft * The term Scale feems to have been derived from the fteel-yard, and its notches or divifions marked on tl>e beam, to adjuft the different degrees of weight by. dimenfiou ( ^5 ) dimenfion of the piece you would draw. Secondly, divide one of thefe parts, which you luppofe to be a foot, into twelve equal parts, the number of inches in a foot ; to efFe£l which, divide that part or foot into two equal parts, as at 6 : draw then the two lines 6.1, 6. i 2, and the foot will be divided as required, and in the moft accurate manner, as is clearly demonftrated by the fmall di- vifions on the line 12, each of which are perpendicular to their refpedlive numbers on the oblique lines. To ufe the Scale. If you want one foot one inch, place your compafs foot on the lecond line from the bottom, over i, and extend the other foot to No. i on the fame line. Again ; if you want one foot two inches, then place the foot of your compafles on the third line from the bottom, and extend the other foot to No. 2 on this line. Laftly j if you want three feet feven inches, place one foot of your compafles on the fixth line, over 3, and extend the other foot to No. 7, and fo on for any other number of feet and inches that may be required. On the ConJlru6lion and Ufe of a Scale of Tenths. Draw eleven lines parallel to each other, and at equal diftances, as in Fig. 10, Plate II. Afterwards lay down eleven divilions, as you fee on the fcales found in cafes of inftruments (I have divided mine only into fix, for want of room). Take one of thofe divifions or parts, and by Prob. I. Fig. i, divide it again into ten equal parts, placing the divifions on the bottom and top line. Then from the point draw a line to the point 1 on the top line, and fo on, as the Figure fhews. When all thefe lines are drawn, there will then be precifely one hundred equal parts, diftinguifhable by the dots on the feveral angles of the rhombs, becaufe, being divided into ten each way, they multi- ply into one hundred, by which we fhall be able to take any tenth or any hundredth part of the large divifions or integers, i, 2, 3, 4, &c. D To ( 26 ) 'to uje this Scale, If you want one of the large divifions and one loth, this is afcertained by- placing one foot of your compafles on No. i, and extending the other to the firft divifioa beyond o, and fo on, as may be required. Again, if you want one large divifion (which may be called a foot) and eight hundredth parts of a foot, place one foot of your compalTes on the line 9, and extend the other to the firfl tenth on that line, and you will then have one foot and ei^ht hundredth parts, as required. Laftly, if you want five feet, five tenths of a foot, and five hundredth parts, place your compafs foot on No. 6, on the right hand end of the fcale, which is the fixth line from the bottom, and extend the other foot to the fixth dot on the fame line, as at 0, and the required dimenfioii will be obtained. It will be evident, therefore, by a little reflection on the nature of this fcale, that any tenth, or hundredth part of a foot, may be ac- curately taken ; for it is evident that, by this method, the whole fpace, com- prehending what we may fuppofe a foot in length, will be accurately divided into one hundred equal parts. The fcale of chords comes next under confideration. This fcale is com- monly found on the contrary fide to that whereon the fcale of tenths is marked, which we have now defcribed. The ufe of it is to lay down angles of different degrees, and to divide a circle into various proportions and parts. 'the ■ConfiruSiion and Ufe of a Scale of Chords. 1. Open the compafles to fixty degrees on the fcale marked C H O, Fig. 11, Plate II. and by this opening defcribe a femicircle, as B D A, - Fig. 1 2. Then if the arch B D be divided into ten equal parts, thofe parts lo, 20, 30, &c. will anfwer to 10, 20, 30, &c. on the fcale of chords, Fig. 11. Hence, if you want to divide a circle into twelve parts, take thirty from the fcale of chords, and apply the compalTes to the arch B D at 30, then B D will contain it ( 27 ) it three times, and confequently the whole circle will contain it twelve times. If again you want this circle divided into eight equal parts, then from the fcale take the chord of 45, and apply it to the arch BD at 45, and this will divide the quadrant into two equal parts, and therefore the whole circumference may, by the fame opening, be divided into eighths. In this manner any other di- vifion of a circle may be certainly known at once, which a little thought will eafily make clear, and therefore it is unneceflary to give any other example on dividing the circumference of a circle into equal parts. This fcale may likewife be ufed in laying down any angle* not more than ninety degrees. Draw the line Go, Fig. 16, at pleafure ; then take the chord 60° and defcribe the arch 00 at pleafure. With your compafles take the chord 37°f and place it on the arch 00 ; draw the right line G 0, and you have an angle of thirty-feven degrees and an half, and fo of any other, to ninety degrees. On the PROTRACTORf. The Protraftor is a femicircle of brafs, divided into one hundred and eighty degrees, by the help of which we may defcribe an angle of any afligned quan- tity whatever, and likewife meafure any angle already laid down. Let the arch, divided into one hundred and eighty equal parts, on the line AB, Fig. 6, Plate I. be confidered as the bpafs protradlor, which is found in common cafes of inftruments. * Angle. " This feems to be from AfKuXoy, ankulos, the bending of the elbow;" and in Geo- metry, implies the point in which two lines meet: but the quantity of an angle is the fpace compre- hended between the two lines meeting in a point, as 0, Plate II. Fig. 16. and its proportion is ex- preffed by degrees ; which term, Degree, means fimply the three hundred and fixtieth part of a circle, whether great or fmall. t Protrailor, {xom protraflum, " to draw out in length;" accordingly, by the help of this inftru- ment we may draw out the legs of a triangle to any length we pleafe. D 2 Firft, ( ^8 ) Firfl-, Obferve the center of the protrador, diftinguifhed by a fmall notch 9n the diameter, anfwerable to 6, on A B, Fig. 6- 2d. Let it be required to lay down an angle of ninety degrees, and let A B be confidered as the bafe. Then place the fmall notch on the diameter of the brafs protradlor, upon 6, on the line A B, and make a mark exadlly over 90 ; confequently a line from 6, the center, to 90, the vertical* point, will form an angle of ninety degrees, or what we commonly call a fquare. Again, if an angle of forty-five be wanted, proceed as before, and make a dot over 45 ; to which draw a line from the center, and it will be an angle, as required} and fo of any other to any quantity. This is fo plain, that to fay more would be necdlefs. It may however be proper to obferve, that the quantity of any angle already laid down may alfo be found by the protrador, as follows : Let Goo, Fig. 16, Plate II. be the angle to be meafured. Take the ra- dius, or half diameter of the protraflor, and defcribe the arch ; then open the compaffes to 00, and apply them to the degrees marked on the inftrument, and it will immediately be feen how many of thofe divifions are contained in the ano-le, which number of divifions are called the quantity of the angle. Or thus : place the center of the protraflor to the angle G, and let its adge coin- cide with either of the lines G 0, and in what degree on the protraftor the other fide touches will be the quantity of the angle. On the Sector -f-. The Seftor is a moft univerfal inftrument, and ufed for various purpofes in the different branches of mathematical learning. Nor is it without its ufeful- * Vertical, " placed in a dire£l:ion perpendicular to the horizon." + Seder ; it is fo called becaufe, when it is opened, it comprehends a portion of a circle between two femidiameters, making an angle at the center, as OA4, Plate I. Fig. 6. nefs yj /)/ /. Frflt/emah'/xi/ Sutures /(5r ,//i;'J,,i,; /ti. 2'ulil^Ai/aS'^ieAct ii'fVcArAug^ S7. 779/. ( ^9 ) nefs in the art of drawing, and therefore thofe who are concerned with defign- ing, ought, in fome meafure, to be acquainted with it. To this end let us iirft confider the moft fimple part of it, which is, to di- vide any given right Une into any number of equal parts. The line to be divided by the fe^tor is 7.7, Plate I. Fig. 5, which is to be divided into feven. Firfl:, Look for the line of lines on the fe6lor, which may be found by ob- fervins two brafs centers marked with l on each limb of the inftrument. *D Second, Take the length of the line 7.7 in your compafTes, and place one foot on the point 7 on the line of lines, and opening the Se£lor, extend it till the other leg of the compafles coincides with the point 7 on the other limb of the inftrument, as Fig. 5 clearly expreffes. In this pofition keep the fedor, and moving the compafles to i.i, which is the neareft figure to the center of the inftrument, conrrafl: thsir legs till ynii take the opening 1. 1, which, if corredtly done, will be one feventh part of the line 7.7, as propofed. Perhaps it may be required to divide a line into fourteen ; if fo, then as there are only ten on the line of lines, you take half the length of the given line in your com- pafles, and place their legs on the points 7.7 as before ; and, as this opening is but half the length of the line to be divided, the compaflTes muft be contra£led to I.I as before, and then the line will be divided into fourteen, becaufe twice feven is fourteen. Take this in a numerical fenfe, and confider the line 7.7 as 70, to be divided by 10, and the quotient may be found on the {eStor thus : extend the compafles from the center of the joint of the fedor to I on the line marked L. And with this opening of the compafles place one leg in the brafs center L, and extend the other limb of the feftor till the other leg touch L. With this opening of the fedtor, take the compafl*es and con- trad them till they coincide on y.j on the fame lines. Laftly, apply the compafles at this opening from the center of the joint as before, and it will extend to number 7, that is, feven of the fmall divilions or tenths, which will be the quotient fought for ; for if we fay, How often ten in feventy ? the an- fwer ( 3<^ ) fwer is, 7 times. The whole of this is more mathematically expreffed as fol- lows : to work a queftion in divifion by the line of lines, extend the compaffes laterally from the beginning of the line to 1 ; and open the fe£tor till that ex- tent coincide with the parallel of the divifor, as in this cafe 10.10 ; after which, by this opening, take the parallel of the dividend 70.70, which mcafured la- terally* will give 7 the quotient. This I only confider as a hint of what may be done on the fedor. Of the Line of Polygons f on the SeSor. This line is intended to divide the circumference of a circle into equal parts, by which various kinds of Polygons, from a pentagon to a duodecagon, may be formed. Hence it is diftingui(hed by the letters P O L on this in- flrument. Let it be required to divide the circle. Fig. 8, into five, which forms a pen- tagon. Take the radius or half diameter of Fig. S, and opening the fprftor, aS defcribed by Fig. 7, place the compafs on the point 6.6, marked radius. In this pofition keep the le61:or, and, without any variation of the inftrument, you may divide the circle 8 from 4 to 1 2. In the cafe before us it is into five ; therefore take the compaffes from the points 6, and extend them till they touch 5.5, and this opening will go five times on the circle 8, as will be evident if you take ^.c^ in your compaffes from Fig. 7, and apply it to Fig. 8. Laflly, if you want the circle 8 divided into twelve, by which to form a duodecagon (fee Plate II. Fig. 26), the fedor ftill remaining unaltered, place * The term lateral, applied to the fe6lor, implies that the meafureir.ent be taken perpendicularly to the horizon, or periphery, which is defcribed by the motion of each limb of the fedlor ; but pa- rallel meafurement on the fedor, implies an extenfion of its limbs, and an application of the legs of the compaffes to fuch numbers as are of equal diftance from the center or beginning of the line of lines. t " Polygon, from ircAuc, polus, many; and ywwa, gonia, a corner; having many corners or angles." your (i 31 ) your compafs legs on the points 1 2.12, and apply them to tlie circle 8, and it will be divided as required. Obferve alfo, that a geometrical fquare may, by the fame means, be infcribed in any circle ; for by keeping the fe£lor extended as before, and opening the compafTes till their legs touch on 4.4, this opening will turn four times on the circle 8,, and therefore will form a fquare. How this line of polygons is divided fo as to proportion any circle in this manner, will eafily be underftood by confidering Fig. 6. Defcribe a circle of any radius, and draw the diameter AB. Divide one half of the circumference into one hundred and eighty equal parts, called degrees, and from 90° draw the arch 4 from the center A, then will the lines AO and A 4 reprefent the limbs of the fedlor, Fig. 7, and the fpace 4.0 on Fig. 6 will anfwer to 4.4 on Fig. 7.. Next draw the arch 5 from 72°, and from the center to 5 will be the chord of 72°, thp degrees rnntained in the fide of a pentagon, anfwerable to 5.5 on Fig. 7. Proceed to the arch 6, and obferve, that this is the radius of the circle, and is always equal to the chord line 60°, and therefore contains a length equivalent to the fide of a hexagon, or a (ix-fided figure, and agices with 6.6 on Fig. 7. After thefe remarks, I think it unneceflary to go through each chord line; only the reader ftioulci obferve, that I have marked luch chcrds as have frac- tional parts on the fine lines, or thofe drawn perpendicularl}' from AB. For inftance, the chord for a heptagon is fifty-one degrees and three-levcnth parts of a degree; and the meaning of three-feventh parts is nothing more than to divide a degree into feven, and to take three of thofe parts and a^'d to fifty-one, which is exactly the fide of a circle divided into feven, c^llc^i a heptagon. Thefe parts are eafily found and proved by dividing three hundred and fixty, the ( 32 ) the number of degrees contained in a whole circle, by the quantity of fides contained in any polygon, for then the quotient will be the number of degrees which are in the arch of e.very fuch chord line. Thus for a heptagon : divide three hundred and fixty by feven, then will the quotient be fifty-one degrees and three-fevenths, equal to the fide of a heptagon. Of the Line of Chords on the Secior, The chords on the fixed fcale have already been confidered (fee page 26). Thefe chords are limited to one circle, which, to fuit that fcale, mufl always be drawn by the compafles extended to fixty degrees on that fame fcale : but the fcale of chords on the fe6lor is unlimited, becaufe the chords of circles of various radii may be found according as the limbs of the inftrument are more or lefs extended. The line of chords is on the fame lide of the "ledtor with ^the polygons, marked with C nigh to a brafs center on each limb : and if it be required to find the chord of thirty of any circle, take the radius of the given circle, and open the fedor till the compafs legs coincide with thofe brafs centers at 60.60, then contracting the compafles till their legs touch 30.30, the required chord line will be found. In this manner proceed in any other cafe; always ob- fervint^ that the femi-diameter of the circle muft limit the opening of the fedlor at the brafs centers. By this line of chords on the fedlor it is evident that a circle may be divided into feven hundred and twenty equal parts with confiderable difpatch and great accuracy. Of ,\:"l'. /'/./. Sct/fe of 7e/if/i^. C/}or(/s. St't/ns. ^-.c ^/c,//,- /•/ i'/,lll/(. ^/'^^f/ . // Thtr -i. to 10 .J To AtfH' ixn Oraf fy^eSccrorand JZ7M' to mifre a(h- -reWp, ofitrffenytf projetti'ons . ff — * S J J 2 r A y rli/<'r/,j f/i <■ //tip, /(■//( ■y/(/fl ,r. J, \ //i,7i < J*ti7 V ilh/i>ifrurn -/.J'/U-ra/-cn tic/ /. fhi-^'f ^t'r/^//'. TiJ'///JlJ ,u- r/le ^4,-t ,iirn^.r. .-luo-. '--jfi. /-.//. ( 33 ) Of the hint of Sines on the SeSlor. A Sine is a right line drawn from one end of an arch perpendicularly upon the diameter drawn from the other end of that arch, as the perpendicular line 90, drawn from the diameter B A, Fig. 12, Plate II. is the fine of the arch BD; and fo likewife all the other perpendicular lines, as r, 2, 3, 4, 5, &c. on the line B A, are fines of fo many different portions of the arch BDA. The line of Sines on the feftor, which Fig. 13 is intended to reprefent, is marked s s nigh 90.90, with two brafs centers, one on each limb of the in- ftrument. The feveral divifions on this line, marked 10, 20, 30, &c. anfvver to thefe perpendicular lines i, 2, 3, 4, ^.,^c. on the line BA, Fig. 12, and the different fituations of thofe perpendicular lines are found by dividing the arch D A into nine equal parts. Perpendiculars being then drawn from each refpe£live divifion on the circumference of the circle to the diameter AB, they are of courfe denominated fines of 10, 20, 30 degrees, and fo on. to draw an Oval by the SeSlor. Firfl, Draw a circle that will comprehend the longcft diameter of the oval you wifh to defcribe, as the circle BDA, Fig. 12. Divide the quadrant DA into nine equal parts. Second, Take then the fhortefl diameter in the compafTes, and place one foot on the fine 90", and open the fedtor till the other coincides or touches 90* on the other limb of the inflrument. In this pofition keep the inflrument fixed, and contrail the compafTes till their feet touch the fine 8o°.8o°; transfer this opening of the compafTes to the perpendicular line 8 at 80, which mark with the point of a pencil. Proceed to the fine 70, keeping the fe£tor flill in the fame pofition, and, after contrafting the compafTes till their legs touch 70.70 on the fedlor, tranf- E fer ( 34 ) fer this opening to the perpendicular line 7 at 70*, and fo on of all the reft to the fine 10, by which will be obtained nine points, contrafted in due propor- tion * from the arch DA; and a line, paffing through each of thefe points, and drawn by a fteady hand, will form an ellipfis perfedly true and agreeable, as is evident by the figure. From what has been faid, I prefume it will eafily be underftood by every one how to proceed with the other quarters to complete the whole ellipfis. A circle may alfo be defcribed by the fe£lor upon the fame principle that an ellipfis is drawn by it. This, in itfelf, is not very neceflary to be known, becaufe when we have no compafl!es, no ufe can be made of the fe6lor, and when we have them by us, they are the beft inftrument for drawing a circle. However, fince what belongs to the drawing of a circle by the fedlor, partly belongs to the defcribing of an ellipfis by this inftrument, I fliall venture upon this Problem. Operation. — Draw a right line at pleafure, of length enough to contain the diameter of the circle to be drawn. Bifei!! -j- this line, and draw a line at right angles with it of the fame length. Take then the femi-diameter of the circle, and place it on the lines each way. Open the fe<flor, and on the line of fines proceed as before to take the fine 80. Transfer this to any femi-diameter, as 9 A, Fig. 12, which will extend to 1 on that line. Then proceed to take the fine 70, and transfer this alfo, which will extend to 2 on that line. Proceed to the fine 60, and this opening will * This is evident by obferving, that as a right line drawn from 45 on the tangent line to the center g, cuts the arch DA in the degree 45; fo likewife will a right line drawn from 10 on the tangent line to the center, cut the elliptic arch 90 A in the fame degree. + A line is faid to be bife£ted when it is divided into two equal parts, from "Us znd/eflum, to cut in two;" an operation which is eafily performed by defcribing two arches from the extremities of the line to be thus divided; as from b and d, in Fig. 14, where two arches intcrfedt, which, if a line be drawn from thefe interfeftions, it will both bifed the given line, and will at the fame time be drawing one at right angles to it. extend ( 35 ) extend to 3 on the fame line, and fo on, till you take the line 10, which will extend from 9 to 8. The fame muft bs done on the other radius, as you take the fines from the fedor. Having thus divided one diameter, draw perpendi- cular lines from each divifion each way at random. Laftly, take the fame fuies again from the line 9 A, and place them upon their refpedive fines ; that is, take from 9 to i, which is the fine 80, and place this upon the perpen- dicular line 8 at 80, and fo of all the reft, and they will form thirty-fix points for the whole circle; through which points, if a line be corredlly drawn, the circumference of a complete circle will be produced with as much accuracy as when we draw the circumference of an oval in the fame manner. Of the 'Tangent * Line on the Senior. A tangent is a right line drawn perpendicular on the extremity of fome radius, touching the circumference of the circle, but not cutting it, as A 45, Fig. 12. This line is of ufe to divide the circumference of a circle into any number of equal parts, and may be found on the fe£lor by a brafs center on each line, marked T. To this line there is added another of the fame kind, marked T on each limb, but without a brafs center to it. To divide a circle by this line, proceed thus : Take the radius of the circle to be divided, and with this opening place the compafs legs on each line T, marked 45.45, then will the fedlor be pre- pared for finding every degree of a circle up to 45. This is clear; for if the radius be laid down on the tangent line, Fig. 12, as at 45, a line drawn from 45 to 9, the center, will cut the arch DA at 45 degrees, as is obvious by infpedion. Thus the circle may be divided into eight, fince forty- fiye is the half of ninety, confequently the eighth part of three hundred and fixty. The * Tangent, from tangens, Latin, touching. E 2 fedor ( 36 ) fedlor being ftill in the fame pofition, if you want to cut the arch DA at lo degrees, contrafl the legs of the compafles till they coincide with ro.io on the tangent line, and transfer this on the tangent line A 45, and a right line being drawn to the center as before, it will cut the arch D A at 10. Hence if the arch DA is required to be divided into nine, the extent of the compafles at thofe ten degrees will turn nine times on the arch DA. It has already been obferved, that there are two tangent lines on the fe(5lor. The tangent line which has not the brafs center, is to increafe that which has one up to y^j as it is marked on that line. When therefore any degree above forty-five is wanted, take the radius of the circle to be divided, and open the ledor till the compafs legs touch 45 on the fecond tangent line on each limb; then will the inflrument be prepared for taking the tangent of any degree up to feventy-five, by proceeding in the fame manner as on the firft tangent line. SECTION III. On the Names and Properties of various ufeful Geometrical Figures of the Superficies. To have fome knowledge of the names of ufeful geometrical figures is cer- tainly of advantage to every one, and efpecially to fuch perfons as are concerned •with drawing or making pieces of work of the like forms.. It is certain from experience and matter of fa£t, that many, not acquainted with names of this kind, are obliged to ufe a dozen words and figns when one would be fufficient. Befides, a knowledge of thefe names, together with an acquaintance with the ( ^7 ) the general properties and manner of drawing fuch figures, muft certainly be confidered as an introdudlory flep to a more advanced knowledge of Geo- metry, by thofe young men who intend to rife higher in this fublime fcience, than can be expefted to be taught in a drawing-book. I (hall therefore begin with the names and properties, and afterwards defcfibe the conftruftion or manner of drawing, the moft generally ufeful jfigures. Of the Superficies*. (See Plate II.) No. r, is a Geometrical Square, fo called becaufe it has four fides of equal length, and four right angles. Noi, 2, is a Parallelogram. This figure receives its name from its oppofitc fides and ends being all parallel to each other. No. 3, a Rhomb, which is properly a geometrical fquare moved out of its pofition, fince all its fides are equal, but not its angles, two of them being acute, and the other obtufe. No. 4, is a Rhomboides, a figure which bears the fame affinity to a paral- lelogram that a rhomb does to a geometrical fquare. A rhomboides has its fides and ends parallel to each other, but its angles differ the fame as thofe of the rhomb ; and therefore a rhomboides is a parallelogram moved out of its proper formf. No. 5, is a Trapezoid, which has four fides, two of which are parallel, and two not, the fame as the feats of fome chairs. * Superficies, fuperficies, Lat. the furface or outermofl: part of any thing, and in Geometry are fuch figures as are bounded by one or more hnes, or an extenfion which has length and breadth, but no thicknefs. t Thefe four figures are all parallelograms, though of different names. No. 6, ( 38 ) No. 6, a Trapezium containiug four fides, which are all unequal, and none of them parallel. Thefe fix figures, being all of them bounded by four right lines, are, by geometricians, called quadrangular or quadrilateral plain figures. Of various Triangles. No. 7, is an Equilateral Triangle, fo called becaufe all its fides are equal to one another; and, as every triangle contained under three equal fides, whe- ther circular or mixed, is called equilateral, fo the figures ii, 12, 15, are alfo of that denomination. No. 8, is a Right-angled Triangle, becaufe two of its fides are perpendicular to each other, and confequcntly make an angle of ninety degrees, as the line 9.90°, Fig. 12, is perpendicular to BA; therefore A 9.90° forms a right- angled triangle, comprehending a part of a circle equal to ninety degrees. In all ri^ht-angled triangles, the fides containing the right angle are called the Legs, as the fides 9 A, A 45, are the legs of the triangle 9 A, 45, in Fig. 1 2 : and the oppofite fide to the right angle is called the Hypothenufe, as the line 9.45, in the triangle 9 A, 45, is the hypothenufe fide of that triangle. •' The perpendicular height of any triangle is a line drawn from the vertex to the bafe perpendicularly :" thus if the triangle PRO, Fig. 15, be propofed, P O muft be confidered as its bafe, and confequcntly R its vertex ; and if from R you draw the line R P perpendicularly to P O, then the line RP is the height of the triangle RPO, ftanding on PO, its bafe. No. 9, is a triangle called Scalenous, becaufe none of its fides are equal, nor its angles alike in quantity. A Scalene Triangle is compofed of two kinds of ( 39 ) of angles, one obtufe and the other acute ; fo alfo a right-angled triangle is compofed of two, a right one, and an acute. All other triangles are of the acute kind. An obtufe* angle is one that is greater than ninety degrees, or more than what we call a fquare, as a line from 9 to the point D, Fig. 1 2. An acute angle is lefs than ninety degrees, as a line from 9 to 10, confider- ing the fide 9 A as their bafe. No. 10. This Triangle is called Ifofceles, becaufetwo of its fides are equal in length, as G 0, G 0, Fig. 16; or if the feftor be opened, a triangle of this kind is fitly reprefented by it. Thefe four triangles, being bounded by three right lines, are called re£li- lineal plain triangles; and, in general, thefe are placed before the quadrilateral, or four-fided figures, becaufe by geometricians they are confidered as more fimple, having only three fides : but as triangles generally appear more out of the way to workmen, I have alTumed this liberty to place them after four- fided figures. Of mixed 'Triangles. Of this kind are numbers 11, 12, 13, 14, and they are called mixed trian- gles, becaufe fome of their fides are right lines, and fome curved ones. Three of thefe are equilateral, or equal-fided, if meafured by a right line; and No. 14 is a fcalene triangle by the fame rule, as none of its fides are equal. The fides of thefe mixed triangles that are round, are called convex tj but thofe that are hollow, as No. 13, 14, are called concave. * Obtufe, fignifies flat or blunt ; and acute, {harp or cutting. t Convex is properly applicable only to any folid that has a curved or fwelled furface, and concave is the contrary. Of ( 40 ) Of Spherical* Triangles. A fpherical triangle is one that is curved on every fide, as No. 15 and i6. Thefe are both of the equilateral kind, becaufe their fides may be bounded by right lines of equal length. Of Mixiilineal Figures. No. 17 is of this kind; and every other figure that is bounded both by right and curved lines is called mixtilineal. o' Of thefe figures fome are regular, and fome irregular. When a figure of this kind is compofed of equal curved and equal right lines, then it is called a regular compound mixtilineal figure ; but when its fides and ends are formed of unequal curved and unequal right lines, then they are called irregular compound mixtilineal figures. Of this fort is No. 18. Of Polygonal Figures. All Figures bounded by more than four right lines are termed Polygons. The figures included between No. 19 and 26 are all of this denomination. But each of thefe figures has its particular name from the number of the fides of which it is compofed. * Spherical, fomething like a fpliere or globe. No, 19, ( 41 ) No. 19, Is therefore called a regular Pentagon i*, becaufe it is bound by five right lines of equal length, and of equal angles; but if any of thofe lines were unequal in length, then it would be termed an irregular Pentagon. The fame might be faid provided the fides were of equal length, if the figure were fo diftorted or pufhed out of its regular pofition as to caufe inequality in the angles. The fame diftindlion is applicable to any other Polygon in the like cafe. No. 20 is termed a Hexagon, 21 a Heptagon, 22 an Odlagon, 23 a Nonagon, 24 a Decagon, 25 an Undecagoni 26 a Duodecagon, > becaufe it has < 6 fides or angles. 7 8 9 10 II >- 12 No. 27, is a figure fo well known that it is unnecefl[;\ry to fay pny thing about it. The fame may be faid of the Semi and Quadrant, Nos. 28 and 29, the one being an half, and the other one-fourth of a complete circle. No. 30, is called the Greater Segment f of a circle, becaufe it is the great- eft part of a circle cut in two by a right line ; and of courfe No. 31 is the Lefler | Segment, becaufe it is not equal to a femi. But if we fpeak of a fegment without regard to comparifon, it is a figure contained between a chord and an arch of a circle. * Pentagon, from *ev7e, penie, five, and ymia, gonla, a five-cornered figure. The other Polygons have all their particular names formed in the fame way, from the Greek numeral adjedlives. + Segment, from fegmentum, a piece cut ofF. X Leffer. This way of forming the comparative adjective is by Dr. Johnfon and Lowth confidered as barbarous ; but as cuftom has fo long prevailed in the ufe of it, and as the car feems to prefer lefler rather than lefs, I thought it would fuit the readers beft to retain it. No, 32, ( 42 ) No. 32, is aa EUipiis*, commonly called an oval. This figure may be confidered, in one view, as produced by the feftion cf a cone, or cylinder, by a plane cutting both fides of the cone or cylinder obliquely to their bale. In another it may be conceived as a circle comprefled at oppofite points in its cir- cumference, by which one diameter is diminifhed, and the other proportionally lengthened. It may alfo be obferved both of a circle and an oval, that they are the only regular fuperficies that are bounded by one line ; and thofe which are bounded by two, are their refpedlive fegments : as Figures 28, 30, 31, 33^ 34. No. ^2, is the Semi-Ellipfis, or Half-oval; and it is faid to be on the tranfverfe axis, when the right fide is equal to the longeft diametep; but when it is only equal to the fliortefl: axis, then it is faid to be on the conjugate, as No. 34. No. 35, is termed an Hyperbolic Figure. When a cone, Fig. 12, Plate IV. has a fedion parallel to its axis, the curved boundary produced by the fec- tion is an Hyperbolic Figure ; and when its fedtion is parallel to the fides of the cone, then the curved boundary produced is called a Parabolic Figure. S E C T. IV. Of the manner of drawing various ufeful Geometrical Figures. In the preceding fe£lion, the names and fome of the properties of the moft generally ufeful fuperficies have been confidered ; and I fhall now defcribe * EUipfis, from iXXh^k, elhpjts, a defeft or omiflion. If a fuperfice be apparently round, but on meafuring it, if one of its diameters be found Ihortcr than the other, there is then a defetl, and wc fay that the figure is elliptic. the ( 43 ) the method of drawing them. However, in doing this it will not be necef- fary to defcribe every particular figure, fmce the fame operation for one will fometimes apply to various others. Prob. V. Fig. 14. To draw a Geometrical Square. By the fecoud method of Prob. III. raife a perpendicular, as E^, Fig. 14, Plate II. then extend the compaffes equal to the fide of the propofed fquare. « Fix one foot in E, and defcribe the arch ^, d, which will cut the line E ^, E </, equal to the fides of its fquare. Laflly, from d and b^ with the fame opening of the compaffes, turn the other arches, and their fedtion will form a perpendicular to the points b and d^ by which the fquare may be completed. From what has been faid, it will eafily be underftood how to draw a Parallelogram. Prob. VI. Fig. 2 and i6. To draw a Rhomb. if the fides of this figure be intended to Incline at an angle of fixty degrees, all that is necefiary is to draw two equilateral triangles from their oppofite bafesj and to draw an equilateral triangle is nothing more than to take in the compaffes the given fide of the triangle, and from a right line turn an arch each way, as Fig. 2. Plate I. and their fedion, as at E, by lines drawn to it, completes the figure. F 2 Then ( 4+ ) Then if a right line be drawn parallel to C D at E, and c dbe laid on this line fuppofed to be drawn, it will complete the Rhomb. The Rhomboides, being of the fame fpecies of figure, is eadly drawn by the fame rule. Nor is it requifite to defcribe the method of drawing any other of the figures till we come to the Pentagon, becaufe fome of them are variable, and thofe that are not fo, are drawn by the fame rules that are applicable to the Square, Rhomb, and Equilateral Triangle. Pros. VII. Fig. 19. How to draw the Polygons. To draw a Pentagon whofe fides (hall be equal to a given length, as the line 12. I, Fig. 19, Plate III. Operation. — Draw a right line 12. i, and take the fide 12. i of the propof- ed Pentagon. Place one foot of the compafles on 12, and with the other defcribe the arch i.i. Again, place the compafs foot on 1, and defcribe the arch 1 2. 1, and through the point where thefe arches meet raife a perpendi- cular line, and continue it at pleafure. Divide the arch 12.1 into fix equal parts. Take then the firft of thefe parts, and defcribe it to the perpendicular line downwards, as the figure clearly (hews ; and from this point on the per- pendicular line extend the compafles to 12, which will be the radius of a cir- cle that will contain 12.1 five times : therefore with the compafTes thus fix- ed, defcribe the circle, Fig. 20. and it will admit of 12. 1 five times, forming a regular Pentagon. And here it (hould be obferved, that what has been done in this Problem for drawing a Pentagon, prepares the way for drawing any Polygon up to 12, whofe fides are equal to 12.1 : therefore in defcribing the other Polygons, I fliali proceed as being thus far advanced. Prob. A-"^!. /./.: J^o/vf/o/is. Ovet/j. .').i J. froki^ J'ai/p r Tui-Piu' t/ir •i'.'.' dtr;rt.r.^l\f,t.''jO. i~,)i.ln ti./h /',''/■//¥?//'// ift"/,' ( 45 ) Prob. VIII. Fig. 19. To defcribe a Hexagon, vvhofe fides fliall be equal to any given length. Operation. — Take 12.1, the fuppofed dimenfion of the fide of the Hexa- gon, and with this radius draw a circle, whofe center is at the interfedion of the two arches 12.1, i.i; then will the radius turn fix times on the cir- cumference of that circle, as the fmall daflies which are on it fpecify. It may be made a general rule without exception, that whatever the dia- meter of a circle be, its radius will always divide the circumference into fix. Prob. IX. Fig. 19. To defcribe a Heptagon, whofe fides (hall be equal to any given length. Operation. — Take one of the parts on the arch 12. i, and turn it to 7 on the perpendicular line. Extend the compaffes from this point 7 to 12. which will be the radius of a circle that will contain the given fide 12. i feven times, which forms a Heptagon. If an OcStagon be wanted whofe fides are equal to 12.1, take from the cen- ter two parts, and defcribe the arch 2.8. Laftly, extend the compaflTes from 8 to 12, which, as before, will be the femi-diameter of a circle that will con- tain the given fide 12.1 eight times, by which an odagon may be formed. In the fame manner proceed with the other to a circle that will contain the given fide twelve times, as the largeft circle in the figure evidently does, as marked by the figures i, 2, 3, &c. In the preceding diredions for drawing the Polygons, their fides are prcvi- oufly determined as to their length ; but the circle that will contain' the fides 1 fo ( 46 ) fo many times, is required to be found. We (hall now change the order, and propofe a given circle, in which ftiall be infcribed any Polygon of the above kinds. Prob. X. Fig. 21. Therefore a circle being given, let it be required to find the fide of a Penta- gon that may be infcribed within the given circle. Operation. — Let the line q 5 be the diameter of the given circle. Bifed the diameter, and draw a line at right angles with it; then with the radius s 5 defcribe the circle. Second, Divide any of the quadrants of this circle into five equal parts, and a chord line extended to four of thefe parts will be the fide of a Pentagon that may be infcribed in the given circle, as the figure plainly (hews. Prob. XI. Fig. 21. To find the fide of a Heptagon that will infcribe within a given circle. Operation. — Let Fig. 21 be the given circle, as before. Divide any of the quadrants into feven, as the under right hand one in the figure. Take then four of thefe divifions in your compafiTes, and the whole circle 21 will contain it feven times, which forms a Heptagon. In this way proceed with the other Polygons, always obferving, that what- ever number of fides the Polygon is required to have, the quadrant of the given circle muft be divided into the fame number of equal parts; and four of thefe equal parts muft always be taken for the fide of the Polygon without ex- ception. - ( 47 ) eeption. This is exemplified on each quadrant of the circle, which has al- ready been referred to, and, by a little infpedlion and refledtion, cannot fail to be underftood. The fimplicity of this method of infcribing Polygons in any circle, makes it highly ufeful to all who are any way concerned with defcribing fuch figures on an extenfive fcale. For inftance, how eafy is it to lay down the plan of any room, or mark out the foundation wall for any building of thefe figures, by firft drawing a circle equal to their refpe6live areas, and dividing the qua- drant of that circle into the fame number of equal parts as the room or building has fides ; and then taking four of thofe parts for each fide of the building or room. From thefe hints the Cabinet-maker alfo will eafily apply this method to any table-top, or other piece of work that is required to be made of thefe figures. Of the various Methods of defcribing Ovals* pROB. XII. Fig. 22. To draw an EUipfis by the interfeftion of two circles. Operation. — Let the line B A be the tranfverfe, or long axis, which divide into three equal parts. Take one of thefe parts for the radii of the two cir- cles, and on the centers^ and s defcribe the circles interfering each other at n n. Draw from n a right line through d to b» From n draw n s to f, and fo of the other fide. Place the compafs foot on «, and extending the other to by turn the arch b e. Laftly, fix the foot of the compaffes on the other », and defcribing the oppofite arch the oval will be completed^ PR0B» ( 48 ) Pros. XIII. Fig. 23. To draw an Oval whofe tranfverfe axis (hall be equal to the diameters of two given circles. Operation. — Draw C D equal to two diameters of a given circle. Defcribe the circumferences of the two circles. Then from the center of each circle, with the compafTes in the fame pofition as when the circles were drawn, turn two arches, s dp and p s, interfe*Sting in the points s and p. To complete the EUipfis, fix your compafs foot on j, and extend the other to n ; turn the arch « r. Laflly, fix the compafs foot on p^ and defcribe the oppofite arch, and the work is done. The method of drawing thefe two kinds of Ovals fuppofes that we are only confined to the length of the long axis, without regard to the fhort one ; but the following Problem is to draw an Oval of any length and breadth as may be required. Prob. XIV. Fig. 24. To defcribe an EUipfis whofe tranfverfe and conjugate axes are pre- determined. Operation. — Let EF be the tranfverfe, and a half the conjugate. Take ^zo half of the fhort axis, and "place it from E to ^. Divide then the re- maining part of half the long axis into three equal parts, as the figure fhews, and take one of thefe three parts and lay it on the other way, as from d to n. Take the diflance from « to 0, and lay it from tog. Extend then the foot of the compafTes from g to «, by which turn two arches each way, inter- fedling ( 49 ) fevfUngcach other zi pq. From q to n draw a right line out at pleafure. Do the fame from q to g, and alfo from p to n and ^ on the oppofite fide ; then will every center be found for each refpe£live arch. From the center fi extend the compafs foot to E, and defcribe the arch E (^ c. Do the fame from the center^, and turn the arch mF i. Laftly, from q extend the compafles to l>, and turn the arch lim; and fo of the other fide, which will complete the El- lipfis as required. Method Second. Fig. H in Plate A fucceeding this. Divide half the tranfverle and conjugate axes into the fame number of equal parts, fuppofe four. From the extreme of the conjugate axis draw right lines through 4, 5, 6, at pleafure. To the oppofite extreme point 2 draw lines from a be, and their interfeftions will be the points required for drawing one quarter of the ellipfis. How to draw the other quarter will follow of courfe*. By the fame method the ellipfis may be infcribed within a rhomb or rhomboid, as ihewn at Fig. E. Prob. XV. Fig. 26. To draw an oval of any length and breadth by means of two pins and a line. The above methods for drawing ovals fuit well for fmall ovals defcribed on paper, or any kind of metallic furface, or when very fmall ovals are wanted to be drawn on wood. But when ovals of a large fize are required, they become Inconvenient on account of their centers. Therefore Cabinet-makers generally make ufe of a tramel, by which any oval from two to about four feet may be drawn, both with more difpatch and accuracy than can be done by any other * See Nicholfon's Principles of Archite6lure. G method. ( 50 ) method. The method, however, which is here propofed, is not without its advantages, fince by it an oval may be drawn as large as we pleafe, both with little trouble and confiderable exadlnefs, provided that materials fufficiently flrong and large enough were adopted for pins and a line. Operation. — Let BD be the length of the oval, and As half the fhort di- ameter. Take then half of the longeft diameter, and place it from A to a till it touch the line as exa£lly at a. Again, take the length as and place it on. the right hand at the pin ; then will the two centers be found in which the pins are to be fixed. Laftly, take a line and put it about the two pins, and bring the ends of the line exadlly to A, at which point fix your pencil or piece of thin chalk, and begin to defcribe in the manner that the hand exhibits, and the pencil, &c. will pafs through the points D B A as required. I have found the preceding method vaftly convenient in marking out the circular ends of a fet of dining-tablesj in which cafe there is always an op- portunity of flicking in the pins at one fide of the board, after a line has beea ftruck to make the edge of the board flraight. Then, after drawing a per- pendicular line by a fquare and pencil from half the length of your dining- table top, proceed as above, and you may draw the femi-ellipfis juft to fuit the breadth of the board, if it is fo required. PROB. XVI. Fig. 27, To defcribe an Oval by Ordinate Lines. Where an oval is wanted to be defcribed on a fmooth furface that wiU net admit of any incifion or rough mark, the following method may be recom- mended. Operation. — Draw the infcribed circle in Fig. 27 on a feparate board or paper, that the compafs-foot may not mark the fmooth furface. Divide one femi- ( 5t ) femi-diatneter of this circle into any convenient number of equal parts. From thefe divifions (fuppofe four) raife perpendicular lines to the periphery * or circumference, which are called the Ordinates of that circle. Obferve, the diameter of this circle is always equal to the conjugate axis of the oval. — Proceed now to draw a line on the fuppofed fmooth furface, on which to de- termine the length of the long diameter; which divide into the fame number of equal parts from the center each way as the femi-diameter of the circle is divided into. From thefe divifions draw lines acrofs, as the figure (hews. Number the ordinates of the circle, as i, 2,3, 4, and do the fame to thofe of the intended oval. Take then the compaffes, and fixing one foot in i on the circle, extend the other to the point where that line touches the circum- ference. Transfer this opening of the compaffes to the lines i.i for the oval, and make a pencil mark at the point each way from the diameter. Take the ordinate 2 from the circle, and place it each way from the diameter on the ordinates 2.2 for the oval, and mark the points with a pencil as before. In this way proceed till all the ordinate lines are taken from the circle and transfer- red to their correfponding ordinates for the oval ; after which nothing will re- main but to draw by the hand a fmooth curved line through each point, and the oval will be complete. Prob. XVII. Fig. i8. To draw an oval by means of a notched piece of wood and a fquare. I propofe this method as a good make-fhift, where a proper tramel is not to be had, and when, perhaps, the method of drawing ovals by the fore- going rules may have efcaped the memory, and no book near at hand to affift it. Operation. — Let // be the long diameter, and take any fquare, by means of which draw the line et at right angles, or fquare v^'ith it. Then notch * Periphery, from wsft, peri, about ; and iptfu, phero, I bear or cany ; which derivation, if I am not miftaken, alludes to the hand bearing the radius about its center, in order to delcribe the circum- ference of the circle. G 2 out ( 52 ) out a piece of thin deal, as ag, to fuit the thlcknefs of the fquare, fo that the bottom of ^ may reft on the furface of the oval, and not prevent a from pafllng in the circumfercncey«f. From the pencil point near a to the end near g muft be equal to half the long diameter gf, and from the notched part a to the pencil point « muft be equal to half the fhort dinmeter eg. Laftly, place your fquare, and with one hand keeping it unmoved on the two diameters, by the other turn the elliptic arch efiox one quarter. Hovv^ to proceed to the other quarters raufl be evident to. every one, and therefore it is unneceflary to fay more. The truth of this method will appear to every one by obferving, that if ^, which is the end of the notched wood or tramel ftick, is moved gradually to^, the internal angle of the fquare, thea will the pencil point be at f^ becaufe from b to the pencil point is equal to fg, half the long diameter : and again, '\i a, at the notch, be gradually turned to g^ the inner angle of the fquare, then will the pencil point be at e, becaufe from a to « is equal ^^, half the Ihort diameter. I have already fhewn the method of drawing an oval by the fe£lor in Sedt. Ill page 38, and therefore I need not fay any thing on it here. Prob. XVIII. Fig. 30. To find the center and two diameters of any oval vi'hofe circumference is al« ready given, and whofe center and diameters are erafed or rubbed out. Operation. — Let mi qg be the circumference of the oval. Draw the right line y at random, and draw mn any where parallel to oq^ by means of two arches, as the figure (hews. Second, Brfe£l the line m n from its interfeflion with the circumference of the oval, as at s, Alfo bifed: oq m the fame manner as at s. Draw the ( 53 ) the line ig through ssy and from where ig cuts the oval, bifeft ig, as at the center s. Third, On the center s defcribe any circle large enough to interfe£l the cir- cumference of the oval, as at the points c l>. Draw the line ci>, and bife£l it, as at « ; then draw the long diameter ai> through us, the center ; and, laftly, draw e d parallel to cl> ; then will edhe the ftiort diameter, al> the long one, and s the center, as required. This Problem will be found ufeful in many cafes. For inftance, when the face of a fire fcreen is a true oval, and it is required to put the brafs fprings on it after being covered with paper or filk, &c. in this cafe it will be very uncertain whether the oval will hang true, if the fprings are only put on by guefs. To avoid uncertainty, take a flieet of paper and lay on the face of the fcreen, drawing a pencil round its circumference, from which proceed to find the di- ameter as above. Pros. XIX. Fig. 17. To find the center of any fegment or complete circle whofe circumference is already given. Operation. — Let BDA be the fegment whofe center is required. Draw the chord lines AD, BD, any how at random. Bife6l the chord AD by defcribing two arches from the points A and D, as the figure (hews. Do the fame to DB. Laflly, draw the right lines ?^ and al> through the interfedions of thofe arches, and where thefe two lines meet in a point, as at c, will be the center as required. It is evident, if c be the true center of the fegment BDA, that it will alfo be the true center of any complete circle of the fame radius. It ( 54 ) It is Ukewife farther evident, that if the chord lines AD and DB were con* lidered as two fides of any regular polygon, the fame method would have the fame effedl in finding its center. The above Problem will be of ufe to the workman, when it is required of tiim to fit up a board into the infide of an arch, in order to afcertain its true curve and depth. To this end, let the line B A reprefent a lath laid acrofs the foot of the arch ADB, to find the length of its opening. Then find the middle of this lath, and from the middle of it put up another perpendicular to it, as D, to find the depth of the arch. After having proceeded thus far, take the board to be fitted up, and make one edge of it ftraight, and draw a line fquare acrofs it, on vs'hich lay on the depth of the arch, as at the point D. From D draw the chord lines DA and DB, bifefting them as has already been taught, and the true center will be found for the curve of the arch ; to which, if it be exadly fawn, will fit the arch ADB, as required. PROB. XX. Fig. 18. To find the diameter of a cylinder, when its ends cannot be mcafured, or of a circular building, when no dimenfions can be obtained from its infide. Operation. — Let the circle, Fig. 18, be confidered as the circumference of the cylinder, and let hk reprefent a ftraight rod, touching the outfide of the cylinder. From any of the divifions on the rod hk put another rod acrofs, till it touch the outfide of the cylinder in a perpendicular diredion from the rod h k ; which is eafily done, by keeping the crofs rod exadly by the fide of the lines drawn fquare, which mark out the divifions. Thus the lines ^/6 and /i, reprefenting the crofs rod, are in a perpendicular direction from the long rod, and are produced till they touch the cylinder. After ( 55 ) After proceeding thus far, take paper, or a drawing-board, as may be re- quired, and draw a right line equal in length to /6X', as /jm^, No. 2. From /ji dvsLW g& and i^ perpendicular to ^k, and of the fame length as ^,6 and ik in Fig. 18. Draw then the chord line gm at random, and from the point m draw mi, the other chord. Bifed thofe chords, as the figure fhews, and where the right lines meet in a point will be the center of the cylinder ; and any right line being drawn through the center s will determine the length of the diameter as required. Thus it is evident that the diameter, and confequently the circumference of any round building, may be afcertained by this method. The lath ^i, in fuch a cafe, may be confidered ten feet long, and five inches broad, becaufe a lath of fuch length would require this breadth to keep it from fpringing in the middle ; and each of the divifions on it one foot : and proceeding in the manner taught above, the mofl accurate dimenfions of the diameter of any fuch building will be found. SECT. V. Of the Names and Properties of various Geometrical Solids — Of the Se£iions of Cones and Cylinders, and of finding citrved Twines to anfwer the Sellions of various irregular Figures. In Sedlion III. page ^6, I have there obferved, that to have fome know- ledge of the names and properties of ufeful geometrical fuperficies is certainly of advantage to every one, efpecially to thofe who are concerned with drawing or making pieces of work of the like figures. 6 With ( 56 ) With equal propriety the fame may be affirmed of the ufeful geometrical folids, the knowledge of vvhofe names and properties frequently enable us to communicate our ideas of the figures of various objefts that occur to us, with greater precifion and freedom than we otherwife fliould be able to do, were we, for want of this knowledge, obliged to ufe a number of explanatory words and figns before we could be underftood. However, I have not introduced more of thefe than what I think quite ne- ceffary to be known, and which I (hall now endeavour to explain in as fhort and clear a manner as I am able. Of the Names and Properties of the General Solids. In Plate VI. No. i is termed a Cube, which is a regular folid, bounded by fix equal geometrical fquares or furfaccs, from Kii/3of, kubos, a dye. It is alfo called by fome a Hexaedron *, becaufe it has fix feats or bafes on which it is capable of being refted. No. 2, is a Parallelopipedon, or Parallelopiped, a regular folid, contained under fix parallelograms, whofe oppofite fides are parallel and equal ; or it is by fome called a Prifm, whofe bafe is a parallelogram. If a piece of wood be feven or eight inches long, three broad, and two and a half in thicknefs, fo plained that its fides are parallel, and cut fo that its ends- are fquare to its fides, then will the piece of wood be of the figure of a pa- rallelopiped. No. 3 is a Pentangular Prifm +, fo called becaufe its ends are bounded by pentagons, or five-fided furfaces, and its fides by five parallelograms. * Hexaedron, from ef, hex, fix ; and i^^a., hedra, a feat, t Prifm, from ^p"^^*, " fomething fawn or cut off," There ^7. /-^>^. J'/urr 0\ J*entajif7uhfr J^riitn Jfcxa/iOitio/' TfLfi TcTftiAfi^/r>/i 0-limicr *'^ ^M>m.fp?h> ,i'p/trrc Ty'raituii fvnoid \^dn'iiht'ib'on -Zce^Fohedi'on I '. 'i|, ' I . :. ! r !■ 'i; fZ/^/f? . 3^ . T^fli^rafpn dej.' JJiH^kx- St'lilp^ JltAAii- rAr.1,1 .Jimb.rr/.r.'SO.jj^i In- h'.lh'rv ( 57 ) There are various kinds of Prifms; as No. 4, is an Hexangular; No. 5, a Trapezoid ical; and No. 6, a Triangular Prifm. An Hexangular Prifm is terminated at its ends by two fix-fided furfaces, and its fides by fxngle parallelograms. If a piece of wood, iev&n or eight inches long, be turned to two or three inches diameter, and if this piece of round wood be planed fo as to have fix fides parallel to each other, then it will be of the figure of an Hexangular Prifm. Again, a Trapezoidical Prifm is one which is bounded at its ends by two Trapezoids (fee No. 5, Plate II.), and whofe fides are four parallelograms, two of which are equal to each other, but not parallel ; and two unequal in width, yet parallel. If a piece of wood be feven or eight inches long, as before, and if one of its fides be about three inches broad, and two of them two inches and an half, inclining or beveling off alike from the fide which is three inches, reducing the fourth fide to two inches broad, then will the piece of wood be of the figure of a Trapezoidical Prifm. Laftly, the Triangular Prifm is fo called, becaufe its ends are bounded by triangles, or three-fided fuperficies, and its fides by three parallelograms. If, as before, a piece of wood be planed fo as to have three fides, fuppofe each two inches broad, and their angles parallel, it will then be of the figure of a Triangular Prifm. No. 8, is a Tetrahedron*, called fo becaufe it comprehends, and is bounded by four equilateral -f triangles. It may alfo be conceived as a triangular pyramid of four equal faces. * Tetrahedron, from fslpa,, tetra, four; and sSpa, as before. t See Plate II. , H Hence, ( 58 ) Hence, if a piece of wood be firft cut into the form of an equilateral trian- oular prifm, and then be ternninated from its bafe till the three fides meet in a point perpendicular to the center of the bafe, and if the terminated or inclined fides be equal in length to their bafe, then will the wood exhibit the figure of the geometrical folid, termed a Tetrahedron. No. 7, is an Oftahedron. It receives its name from the eight equal and equilateral triangles by which it is bounded. It may alfo be conceived as two. quadrangular pyramids, joined together at their bafes. If, therefore, a piece of wood be formed into an equal quadrangular prifm, and if this prifm be terminated from its center each way, till all the fides come to a point perpendicular to the centers of the refpedlive bafes of the pyramids fuppofed to be joined together, then will the piece of wood, thus cut, give the true figure of an Oftahedron. No. 15, is a Dodecahedron, a regular folid, bounded by twelve pen- tagons. To form or conftruifl this regular folid, a piece of wood may firft be turned round, and then planed into ten equal fides. Draw then a regular pentagon (Plate II. Ficr. 1^.) on each end of the piece of wood, one of whofe fides fliall be equal to one of the fides which the wood was firft planed to. Laftly, make five faces on each end of the wood, which fhall comprehend two of the firft-mentioned ten fides, and one of the fides of the regular pentagon drawn on each end ; then will the piece of wood form the figure of a Dodecahedron,, as required. No. 16, is an Icofahedron, which is a regular folid, compofed of twenty equilateral triangles. See Plate II. Fig. 7. This figure may be couftdered as confifting of twenty triangular pyramids, as No. 8, whofe verte-xes meet in the center of a fphere, imagined to circum- fcribe it, and therefore muft all have their heights and bafes equal. To ( 59 ) To conftiufl this folid, a piece of Wood (hould firfl be made round, and then planed into fix equal fides. Upon each fide draw an equilateral triangle, and tlie fpaces between each triangle mu(\: be cut away to the fide of the tri- angle thus drawn ; and when this is done, there will then be four more planes or fiices for four more equilateral triangles, which will make ten. Find the center of one end of the piece of wood, and terminate each fide of the hexagon to this center, and there will be produced fix more equilateral tri- angles, which, added to the other, make fixteen. Find the center of the other end, and terminate the before-mentioned four fides to this center, and other four equilateral triangles will be produced, which will complete the twenty as required. From what has been faid, it is evident that five of thefe folids are regular, fince they may each of them be infcribed within a fphere, fo that each angle (hall touch the circumfcribing fphere in fome point. Flence, to form thefe regular folids, namely, the Cube, Odahedron, Tetrahedron, Dodecahedron, and the Icofahedron, it is prefuppofed, in the above confl:ru£l:ions, that the pieces of wood mentioned are all cubes, whofe fides are equal to the dimenfion of each figure. No. 13, is a Pyramid, a folid whofe fides rife from a geometrical fquare as its bafe, and terminate in a vertical point. As the height of this folid is at pleafure, its fides are fometimes bounded by equilateral triangles, and fometimes by ifofceles, as the figure referred to. Nor are we to confine our ideas of pyramids to fuch only as have fquare bafes, for thefe may be either triangular or polygonal, while yet their refpeftive fines fhall terminate in a point perpendicular to the center of their bafes. The learned are divided in their opinions about the derivation of the term Pyramid : fome think the name is from wuj, pur, fire, becaufe Pyramids afcend to a point like fire ; but others more confidently affirnp, that it is from H 2 _ TTV^Oiy ( 6o ) ■rru^o;, wheat, or com. " Not," fays the author of this laft opinion, " that we are to fuppofe that the Pyramids were ever intended for granaries ; but that the Greeks, when, after many generations, they vifited Egypt, and faw thofe amazing ftru£lures, looked on them as florehoufes for grain ; and knowing Egypt to be a country fruitful in corn, they called them Pyramids — corn ftore- buildings ; being, as they thought, the repofitories for all the pro- -duce of Egypt *." No. 9, is a Cylinder. This is a folid, bounded by two equal circles at its ends, and a parallelogram revolving round their circumference. This figure is fitly reprefented by a garden roller, whence its name kuXh/S^oc, kutendros, a roller; and as for its conflru6tion, it is fo fimple that it is unneceflary to fay any thing about it. No. 12, is a Cone; a folid, bounded by two fuperficies, one of which Is convex, and the other ftraight. The bafe of a Cone is fometimes au ellipfis, and fometimes a circle, and its fides are terminated in right lines to a point perpendicular to the center of its bafe. From this center to its vertical point, a line is fuppofed to pafs, called its axis, on which this body might be made to revolve. And the fame may be obferved of the Cylinder, Conoid, and Sphere, each of which has its imaginary axis, or right line, paffing through its center, about which they may be made to turn- No. 14, is a Conoid ; a folid, which terminates from its bafe to its vertical point in a curved or elliptic direction. Sometimes the curve of its fide is hyperbolic, and fometimes parabolic. See Plate II. Fig. 35, 36. Its bafe, like the Cone, is either an ellipfis or circle. * The bafe of thefe pyramids was equilateral, and meafured 693 Englifh feet. Their height near five hundred feet. They were built in fine marble, and required the labour of tliree hundred thoufand workmen for twenty years. Thefe are inconteftible proofs of the vart numbers, riches, and power, of the Egyptians; as alfo of their fkill in architedlure and the mechanic arts. No. 10, C 6i ) No. lo, Is a Hemlfphere *, which is one half of a globe cut by a plane paffing through its center, and therefore is contained under two fuperficies. No. J I, is a Sphere, or whole globe, which is a body or folid, bounded by one convex furface, whofe parts are all at the fame diftance from the central point, as the periphery of a circle is to its center. Of the Sextons and Coverings of regular and irregular Figures", and how iofnd curved Lines to anfwer their various Sedions. The Se£Hon f of any folid is, when it is fuppofed to be cut by any plane paffing in feme dire£lion through it, which, of courfe, produces a furface or fuperficies confonant to the nature of the fedion, and agreeable to the (hape of the folid which is cut. The fedions of a cylinder are three. — If a plane pafs through a cylinder parallel to its bafe, it will produce a circle, as is evident. Second, if a plane pafs through the center of both ends of it, there will then be produced a paral- lelogram. Thirdly, if it be cut oblique to its bafe, this fedion will produce a furface perfe6lly elliptic. In Plate A, fucceeding Plate III, this is clearly demonflrated, as follows : Let A B, Fig. M, be the diameter of a cylinder, the figure of whofe oblique fedion is required. And let D C be confidered as the feftion propoled, and AD, BC, the fides of the cylinder. Divide the diameter AB into any num- ber of equal or unequal parts, it makes no difference, as at i, 2, 3, 4, 5. From thefe draw lines to the fedion DC, perpendicular to A B. Then, through * Hemlfphere, from o-ipaifa, fphaha, a globe of fphere; and ri'MTus, hemifus, half, i. e. half a globe. t Section, a cutting or dividing; "from feco, to cut." the ( 6> ) the points i, 2, 3, 4, 5, on DC, draw lines indefinitely, but perpendicular to the fedion DC. Take the ordinate i.i from the bafe, and transfer it to i.i' each way on the line DC, and fo of all the other ordinates refpeflively, as the figure (hews ; then will a curve line, pafling through thefe points of the or- dinates, produce a true ellipfis, as is evident ; for D C is the tranfverfe axis, equal to the oblique fe61: ion ; and 3G the conjugate, equal to A B, the diameter of the cylinder. Therefore fuppofe the lines ABDC the boundaries of a plane paffing through the center of the cylinder, and that plane to be divided by parallel lines, as the lines i. r, &c. of that plane ; then it is evident that in whatever ratio A B is divided, into the fame muft the line DC, the oblique fedtion, be divided ; and confequently if lines be drawn through each divifion perpendicular to DC, and if thefe lines be made, refpedtively, equal to the ordinates of the bafe, then would the point i, on the curve DG, if raifed perpendicular to the paper, be perpendicular to the point i on the curve A O of the bafe ; and fo of all the reft. N. B. If the reader cut the curve AOB and DGC through with a knife point, and turn them up perpendicular, he will fee that the points on the elliptic curve will perfedly coincide with thofe on the femicircle. The fedions of a cone are five. — The Triangle, the Circle, the Ellipfis, the Parabola, and the Hyperbola. But as that which produces the ellipfis is of mod confequence, we (hall endeavour to make it clear, that a cone being cut bv a plane oblique to both its fides, will produce a regular ellipfis, per- fectly the fame as that produced by the like fedion of a cylinder. It is natural to fuppofe that a cone (fee Fig. 12. Plate VI.) which termi- nates to a point from a round bafe, would, if cut as above, produce an ellipfis broader at one end than the other. But that it is a regular ellipfis, may be proved as follows : Fif. K, Plate A, is a right cone, whofe vertex is at V, and the center of its bafe at B. The line BV is its axis, and the line qr the propofed fedion of the cone. Divide the fedion yr into any number of equal parts; and 6 through ( 63 ) through thefe draw lines perpendicular to the axis BV, as at i, 2, 3, 4, 5. From thefe feveral lines delcribe femicircles, each of which may be coafidered as a parallel fedlion to the bafe of the cone. From the divifions i, 2, 3, &c. of the fedlion ^ r, draw lines parallel to the axis, or perpendicular to the bafe, till they cut each femicircle refpedtively at i, 2, 3, 4, 5. Now it is clear that thefe perpendiculars muft each of them be an ordinate to their refpeclive circles produced by the feveral parallel fedions ; therefore, from the feftlons q r draw correfpondent ordinates perpendicular to it, and take the feveral ordinates i, 2, 3, 4, 5, and transfer them to the lines drawn perpendicular to the fe6tion qr; and a curve line pafling through thefe points will form a regular ellipfis, when the ordinates are laid on each fide. But it is however neceffary to obferve, that there is one cafe to be excepted, and only one ; and that is, when the cone is cut by a plane fubcontrary to its bafe^as Fig. N, which then produces a circle. A cone cut fubcontrary to its bafe, is when the triangles NAP and S RO are fimilar under their common angle V, the vertex ; for it is evident, that if the bafe of the cone WXP be confidered a circle, then muft the fection line QJT' produce the fame ; for the fedlion Q^T is to the fide of the cone WS as the bafe WP is to the fide of the cone PA. This may be fliewn by lines in the fame manner as in the other cafe. Let the litie be^XS ^^ ^ fedtion of a cone in a fubcontrary pofition. Divide the line eh into equal parts, and through each draw lines perpendicular to the faid feclion, and continue thefe lines to Fig. O. On each of thefe defcribe femicircles to touch each fide, of the cone, as at 5, 4, 3, 2, i. Obferve that the feftion line eb gives the ordinates to each femi. There- fore take from 5 to ^ of that line, and place it from 5 to d^ at O the circle; next take from 4 to c, and place it from 4 to <r at O; then from 310 b, placing it from 3 to ^ at O ; from 2 to «, placing it from 2 to « at O ; laftly, from I to ( 64 ) 1 to O, placing it from i to o; and a curve line through all tliefe points will defcribe a femicircle : for if the compafs foot be fixed on the center 3, and the other extended to ^, it will pafs through each point. '* If a fphere be cut in any manner, the plane of the feftion will be a circle, whofe center is in the diameter of the fphere." But if two planes, or flraight furfaces, cut each other, their common Ccc- tion is a right line. O' I mention thefe particulars, that the reader may more readily and clearly underfland the following Problems. Prob. XXI. Fig. 32. Plate VI. Of finding curved hines to anfwer the Seiiions of irregular Solids. Let Fig. 32, Plate VI. be confidered a folid of the (hape of a vafe, whofe covering and fedtion are to be found ; or, in other words, if a vafe is required to be veneered, how to cut the veneer fo as each joint (hall appear ftraight when the veneer is laid. Operation. — Draw the fhape of the vafe, which, in this cafe, is a femi- ellipfis on the conjugate axis. Draw a perpendicular line through the center of the vafe, which will be the long axis. Divide this diameter into a number of equal parts, and on thefe divifions draw lines parallel to the con- jugate axis, as the figure fliews at 1,2, 3, 4, &c. Draw then on each of ihefe right lines a femicircle, and, for the fake of greater accuracy, let the eighth fpace be fubdivided, by which another circle will be obtained near the renter, as at 9. Draw next a perpendicular line at pleafure, as at No. i. Proceed ( 65 ) Proceed then to take the dimenfions of the curvature of the vafe thus: — place one foot of the compaffes on lo, and extend the other to 9, and with the fame opening of the compafs fix one foot on 10, in No. i, and defcribe the arch 9 at pleafure. Again, fix the compafs foot on 9, and extend the other to 8 on the vafe, which transfer from 9 to 8 at No. i, and opening the com- paffes, fix one foot on 10, and with the other turn the arch 8 at pleafure. In this manner proceed with all the other divifions on the vafe, until its whole curvature is laid down on the perpendicular line at No. i. After proceeding thus far, it mufl: then be confidered how many pieces of veneer will cover the circumference of the vafe, and how broad the veneers may be laid ; which in this example I have fuppofed to be fourteen. Divide therefore each femicircle into feven, as fpecified by the fmall dots on each arch. Upon the femicircle 9 of the vafe, place one foot of the compafles on the point 9, and extend the other to the perpendicular line, which will be half the breadth of the veneer, according to the number of pieces propofed. Take this open- ing of the compaffes and place it each way from the perpendicular line at No. I on the arch 9. Again, on the femicircle 8, take the fpace from the perpendicular line to 8, and transfer this to the arch 8 at No. i, placing it each way from the perpendicular as before. In this manner proceed with the refi:, by which the proper breadth of the veneer on each femicircle will be de- termined; and if a regular curve line be drawn through each point on the feveral arches at No. i, the curved boundaries of thefe arches will be the exadl fliape of the veneers, v^'hich, when properly laid down, will then have the appearance of fo many flraight joints. And hence, by whatever rule or me- thod we find the coverings of folids, regular or irregular, by the fame rule we alfo find curved lines to anfwer their fedionsj for it is evident, if the vafe, after being veneered, was cut through its center perpendicularly, and the ve- neer raifed up again, that its edge would be a faint curve, like that at No, i. Prob. ( 66 ) Pros. XXII. Fig. 33. Plate VI. To find the covering and perpendicular Sedion of a Solid partly convex and partly concave. Operation. — Draw the profile of the folid propofed, as Fig. 33. Let fall a perpendicular from the center of the top. Draw a line through 1 1 parallel with the top, and divide the aforefaid perpendicular line i;ito any number of equal parts, which in this example is ten. Draw parallel lines through each of thofe divifions, and on thefe lines draw fo many femicircles, whofe diameters fliall be equal to the length of each line. Draw a perpendicular at pleafure at No. i. Fix one foot of the compafTes at i on the profile, and extend the other to 2. With this opening fix one foot at i , No. i , and defcribe the arch 2. From 2 on the profile, extend the compalTes to 3, and transfer this from 2 to 3 at No. i. Then opening the compafies, fix one foot at i, and turn the arch 3 at No. i, and fo on of all the other; by which the di- raenfions of the curvature of the profile will be obtained. Laftly, take half the whole fpace from 1 1 on the femicircle to the perpen- dicular line fpecified by the dot, and place this opening of the compafles each way from the perpendicular line on the arch 1 1 at No. i , and mark the places with a pencil. Proceed to 10 on the femicircle 10, and take half of its whole fpace, and place it each way from the perpendicular on the arch 10 at No. 1, as was done on the arch 1 1 before; and in this manner go through the whole, and a fufficient number of points will be found in ordec to draw an irregular curve anfwerable to a perpendicular feiftion of the propofed folid, and which will alfo anfwer for its covering: or veneering. • But ( 67 ) But here I muft obferve to the workman, that in cafe it (hould be propofed to him to veneer any thing of the Hke forms of Fig. 32 and 33, it would not do to cut out the veneers fo broad that fourteen pieces fliould be equal to the circumference. It would require twenty-eight pieces at leaft, before they could be laid down with fafety and eafe, efpecially if it were required that the joints of the veneers fliould be fo clofe as to preclude the neceffity of putting in bringing to hide them. I fpeak this not merely from theory, but pradice, having myfelf veneered knife-cafes of the fame fliape with the figures in the Plate, and where no ftringing was admiffible to hide the joints. But every thinking workman will eafily perceive that it makes no difference in the me- thods of finding the curve lines for the covering, whether the number of pieces be fourteen or twenty-eight. By thefe methods a fphere or globe may be covered, and a curve, anfwer- able to any fedion, through its center may be found. I have not given any example of this on the Plate, as it is prefumed that a few hints will ferve, after what has already been faid on the fubjed. Operation. — Draw a circle whofe diameter fliall be equal to the axis of the fphere to be covered. Divide the femidiameter into nine equal parts, and on thefe parts draw lines acrofs at right angles with the diameter, till they touch the circumference of the circle on each fide. From thefe feveral lines draw femicircles, as was done before in Fig. 32 and 33. Divide the feveral femi- circles into eighteen degrees each, and take one degree from the largefl: femi- circle, and place this opening of the compafles on a right line eighteen times. Then from the extreme points on this line draw arches each way, till they meet in the center of the line. Laftly, transfer half a degree from each femi- circle to their correfpondent arch, laid on each way from the right line, as was done on No. i. Fig. 32; and the whole thus transferred, a curve line pafling through each half degree laid on the feveral arches both right and left from the center line, will form the proper covering for the fphere or globe as re- quired. Obferve, the covering pieces will be of the figure of two fegments of a cir- I 2 cle ( 68 ) cle joined together, and the length of the covering will be equal to half the circumference of the propofed fphere. I muft here entreat leave to remark, that notwithftanding the above direc- tions are addrcfled to men in the wooden way, yet it is certain that the Up- holfterer may avail himfelf from what has been faid on the fubjeft: for the coverings of the like folids made of any kind of ftuff, ought to be cut by the fame methods, and fewed together in feams anfwerable to the joints in wood : but the elafticity or pliablenefs of ftufFs, &c. makes it unneceflary to cut them into fuch fmall pieces as is abfolutely required in wood. Prob. XXIII. Fig. 34. Plate VI. To find the Sedion and Covering of a Knife-cafe whofe front is a double ogee. Draw half the plan of the front, as Fig. 34, and divide the curve of the front into ten equal parts, as the figure (hews. Next determine how much rake the knife-cafe is to have from back to front, by which it will be eafily feen how much the fwell of the front falls at that rate, as the diagonal line 10. 1 (hews in the cafe before us. Draw from 10 a perpendicular line 10 A at pleafure. From the feveral divifions on the curve of the front draw parallel lines till they cut at the numbers on the aforefaid perpendicular. Obferve, that the numbers on the perpendicular line are placed to anfwer the parallel lines as they proceed from each number on the curve of the front. Every thincr beino- now prepared for finding the covering and fedion of the knife- cafe, proceed to No. i, and draw a right line at pleafure, as i.i 1. Take from II to 10, or any other of the divifions, on the front of the knife-cale, and with the compafles repeat it nine times on the right line i.ii at No. i. Then obferve, that from 2 to i on the front of the knife-cafe is rather a wider fpace than the other divifions, which are all equal. The intention of this is, to ( 69 ) to bring the parallel line, which proceeds from 2 on the front, a little farther on from the front line i.i ; therefore take from 2 to I on the, front, and place it from 2 to i on the right line at No. i, then will the whole length from i to 1 1 at No. I be equal to the whole curvature of the front of the knife-cafe, fuppofed to be ftretched out in a right line. On the feveral divifions on the right line i.ii, at No. i, draw perpendicular lines at pleafure. Take in the compafs the fpace i.i from Fig. 34, and transfer this opening to the perpen- dicular line I c at No. i, marking it with a pencil. Then again take the fpace from 2 to the diagonal line at Fig. 34, and transfer this to the perpendi- cular line 2 at No. i, and mark it with a pencil as before. Do the fame from the lines 3, 4, 5, 6, 7, at Fig. 34, and obferve that 11 follows 7, becaufe it proceeds from the point 1 1 on the front of the cafe; therefore take the fpace from II on the perpendicular line to where the parallel cuts the diagonal, and place it on the perpendicular at No. i. Likevvife take 8 and 10 in the fame manner. As for 9, it is loft, becaufe that divifion on the front of the knife- cafe falls on the right line, and, of courfe, has no projedlion. Laftly, through all the points on each perpendicular at No. i, draw a curve line, which will anfwerto the fedion of the knife-cafe, if it be cut anfwerable to the bevel line 1 0.1 on the plan of the cafe. The dark (hade e a b, at No. i, fhews half the veneer or covering of the knife-cafe; and if a piece of ftrong paper be cut double, according to the boundaries of the dark (hade, it will ferve as a pattern to cut the knife- cafe open by, and likewife to cut the veneer by, before it it is glued down. The infide veneer for the front of the top may alfo be cut near enough by it, though it will vary a little; but this defe(£l is not equal to the advantage of having the infide veneer pretty nearly cut to the curve, becaufe it will then glue down much eafier, and be lels liable to fplit. From what has been faid on this Problem, the Ingenious workman may apply the rules and obfervations to other purpoies that may be of more im- portance than the cutting and veneering of a knife-cafe. SECT. ( 70 ) SECT. VI. On various ufeful Problems pertaining to the working Part of both the Cabinet and Upholjlery Branches', as the Methods of mitring Mouldings of dif' ferent Projections — of drawing large Circles, without the Trouble of extending a Lath to their Centers, to defcribe their Circumferences by — of drawing cir- cular Cornices, and fitting up their Valances to them — of mitring the raking Mouldings of Peditnents — the Manner of planning a room to cut a carpet by — and of the Nature andConflruClion of Hip and Elliptic Domes for State Beds. Pros. XXIV. Plate A. Let it be required to cut a number of fleps to their proper lengths, anfwer- able to any given inclination of two fides, as of a ftep-ladder, or the like, without making any drawing, or previous to any part of it being put to- gether, o Take a piece of deal about three feet long and nine wide, and plane it over, making one edg-e of it ftraight. Then confider how much the firfl: and lafl: fteps are to differ in length; which difference, place on aline drawn perpen- dicular to the edge of a board, as 3.1 Fig. B, which confider as the edge, and 1.2 the perpendicular litie; the fpace 1.2 being fuppofed equal to the dif- ference between the firft and lafl: ftep. Take then a pair of compafles, and open them at difcretion, and repeat this opening as many times from i to 3 as there are (leps, fave one; in this cafe eight. From 2 to 3 draw a line, and from each divifion on 3.1 draw perpendiculars to the line 3.2 ; then will each of thefe I, a, b, c, &c. be equal to the refpeftive difference of each ftep to each other. This is clearly proved by Fig. A, which is fuppofed to be a drawing of the ladder at full fize, only for the fake of demonftrating the truth of the method; for we fay that the line 1.2, Fig. B, is equal to the difference be- 7 tween :Nfs. p/ i P/afe^ (^ofiic Sectit>//s. B A E --^.. \ \ /, ^«.1> X \^ V ? \t' "^ 2 ^ \ A \ / \ \>^ >■ ■ M- YS "-■v,XH / V \ \ :[ w ^ /. v< Yv "^ \» 4 V \ ^ 5 / \ c/- B ^^ rs/^r„/,.„./r/ Jit////4i/,i^//,-.l,f ,/')t;/.v/y 17 J>rn:_ J„nr / /^p// r,r ,y.i;^^. ( 71 ) tween the firft and laft ftep, which is twice 1.2 at Fig. A; fo alfo the per- pendicular line a at Fig. B is equal twice a at Fig. A; and confequently the remaining ones are equal to the difference of each refpedive ftep, as the figure will prove by applying the compafles. Or it may be done by taking half the difference, and drawing a line from 4 to 3, which will bifedi each perpen- dicular, and confequently thefe will be equal to a, b^ c, &c. at Fig. A. To find the true bevel for the ends of each ftep, take 1.4 from Fig. B, half the difference of the length of the firfl: from the laft ftep, as at 1.8 Fig. C ; and divide 1.8 into eight equal parts, which is the number of fpaces between each ftep. Draw 1.3 perpendicular to 1.8, and make 1.3 equal to the fpace between the center line of each ftep, as from i to a Fig. A. Laftly, draw from 2, the firft divifion on 1.8 Fig. C, and produce it through 3, and it will be the true bevel for the ends of each ftep. This is evident, byobferving that the aforefaid line 2.3 produced is parallel to the fides of the ladder, and therefore muft be the true bevel required. In cutting the fteps a gauge ftiould be run on the center of each ftep edge, and the reipedive ditFerences of each ftep laid on this line. The advantage of this is, that any thing of the nature of a ftep-ladder, fup- pofing it 20, 30, or any nun;ber of feet in length, may be fet out accurately on a Imall piece of board two or three feet long, provided the width of the board be equal to the difference between the length of the fiift and laft ftep: the length of the board is not limited; for the triangle i, 3, 4, at Fig. B, though vaftly ftiorter than i N 3, at Fig. A, yet both triangles being divided in the fame ratio to each other, produce the fame length in the perpendiculars drawn from each divifion, as will be clear by mealuring the perpendiculars of each triangle. PROB. XXV. Fig. 29. Plate III. To draw an Elliptic Cornice of any given length or depth, and to fit the valance to it. Operation. ( 72 ) Operation. — Let o p he the depth of the cornice with its facia, and make lo half the length of the cornice; draw the quadrant p 2, and divide its chord into nine equal parts, from whence draw lines perpendicular to the bafe of the qua^irant till they cut the circumference. Divide then half the length of the cornice into ten, and draw perpendiculars from each refpedlive divifion, marked i, 2, 3, 4, &c. From the divifions or points on the circum- ference of the quadrant draw lines parallel with the bafe line 10 0, till they cut the perpendicular lines to which they belong; that is, from 8 on the circle draw a parallel line till it touch the perpendicular 8, and from the reft do the fame, which will form fo many points on the refpedlive perpendiculars as will be a fufficient guide for an elliptic arch to pafs through. Obferve, the ninth divifion is fubdividcd, by which another point is gained in the quick part of the ellipfis, for the convenience of drawing the fvveep more perfeclly. The proportion of the hances may be eafily afcertained, as the figure (hews; but in this particular, fiiney will generally be the rule. Method Second. It has already been obferved, that the chord line of the arch 2 /» is divided into nine equal parts, from which lines are drawn till they touch the circum- ference; after which draw the line ^ 9, as a correfpondent chord for the el- liptic curve, and divide it into the fame number of equal parts as the chord of the quadrant is divided into. Then take, for inftance, the length of the perpen- dicular line 8.8 in the quadrant, and transfer this to the perpendicular line 8 on the other chord, and mark it with a pencil. Again, take 7.7 from the chord of the quadrant and transfer it to 7 on the other chord, and mark it as before. In this way proceed till all the perpendicular lines on the chord of the circle are placed on the correfpondent perpendiculars on the elliptic chord, and nine points will be obtained through which the curve is to pafs as before. ( n ) Toft up a Valance to a Cornice of the above Kind. The fluff for the valance fhould be tacked flraight on a board, and with a piece of foft chalk draw a line anfwerable to the line lo o, or bottom of the facia. Divide the facia of the cornice in the manner (hewn in the figure, and draw fquare lines up to the cornice: do the fame on the ftufffor the valance, and take from the cornice the length of each perpendicular line o, 1,2, 3, &c. and transfer thofe different lengths to their refpedive perpendiculars on the fluff, and mark them with chalk, Laftly, by a fteady hand draw, with foft chalk, a curve to pafs through thefe points, which, if accurately done, and cut by the line, mufi: evidently fit at the firft trial. Pros. XXVI. Fig. 31. Plate III. To defcribe the Arch of a Sep;ment of a large Circle, without the afliftance of a lath from its center, nearly true. Operation. — Let Fig. 31 be confidered.a fegment, whofe chord is twenty feet long, and its fwell two feet, as the perpendicular C 10. Draw then a femicircle, whofe radius (hall be equal to C 10. Divide one quadrant into ten equal parts, and into the fame number divide half the chord A C. From each divifion on A C raifc perpendiculars, as i, 2, 3, and fo on. From 9 on the quadrant draw a line parallel to A C, till it touch the perpendicular 9, and mark it with a point. Again, from 8 on the quadrant draw a parallel till it touch the perpendicular 8, and mark it as before; and fo on, from 7 to 7, 6 to 6, till the whole are done. Through the points on the feveral perpen- diculars draw, with a fteady hand, a curve line paffing through thefe points, and it will form a regular arch. It fhould, however, be obferved, that this method, ifpurfued, in drawing a quick curve, will gradually degenerate to a hyperbolic curve, which will be difcernible if the depth of the arch be more than about one tenth of its chord. K Method ( 74 ) Method Second. (On the right hand of Fig. 31.) This method will be found perfed in all cafes without exception. Let ac be the depth of the arch, and a 5 half the chord of the whole arch. Draw c 5, and to this line draw 5.5 at right angles to it. Divide the lines c 5, «5, and 5^, into the fame number of equal parts, and draw the lines i.i, 2.2, &c. Laftly, from i, 2, 3, 4, on- the line 5^, draw lines toe, the cen- ter of the arch, till they touch each correfpondent line drawn through i.i, 2.2, &c. and thefe will form points, through which a curve line pafling will be a true fegment of a circle. For this method I am indebted to Mr. Nichol- fou's Principles of Architedlure, by whofe permifllon it is here inferted. Prob. XXVII. Plate IV. - To take the plan of a Room in an accurate manner, fo that a Carpet may be properly cut by it. Operation. — The room being cleared of ^vtxy obftru£tion, and the floor fwept clean, proceed as follows : Firft, Take a chalk line, and by it ftrike a line parallel to that fide of the room which feems freefi: from irregularities, as dc^ in Plate IV. Then by Problem III. page 25, raife a perpendicular from c continued to ^. Proceed next to the other end of the room, as at d, and by the fecond method of Pro- blem III. if moft convenient, raife another perpendicular continued to a. Draw then a line from a to b, exactly parallel to dc, the oppofite fide of the room. Then will the angles a/Jfd'forma true parallelogram, proportioned to the fize of the room, by which the principal diflortions or irregularities of any of the 3 fides ( 75 ) fides of the room will at once appear. For inftance, the angle v is lomewhat out, as the line parallel to ad phhAy fliews: and in this manner any other angle of the room, whether obtufe or acute, may be afcertained. Second, Let the hexagon end of the room be next confidcred; and let it be obferved, that the plan-taker is fuppofed to have no fquare, or flraioht rule but only a cafe of inftruments and line. Therefore, in order to know how much the fide // bevels off from a fquare, take the line and flrike it by the fide // of the hexagon, and continue the line at pleafure beyond /6. Take then the brafs protraftor, and place the center of its bafe to /, as the figure fhevvs. Make a pencil mark over 90, on the arch of the inftrument, and from z draw a ftraight line acrofs the pencil mark to g at pleafure. Take the fide zVof the hexagon, and place it from i to h. Draw gh parallel to the bafe of the protra£lor, or to be; then will^^ fhew how much //is out of fquare, as required. Examine then the other fide of the hexagon by the fame rule, and if there be any variation from the oppofite fide, it will eafily be difcovered. Proceed to the windows, and find the rake of the jambs in the fame manner as before, which need not be repeated: only obferve, that the protradtor can- not be placed to the architraves becaufe of their irregularity; and therefore it muft be placed on the line ab zt m, after the liney is drawn from the jamb cutting at m. From m draw a perpendicular to e, and make it equal 1.2, the depth of the jamb, and it will, by drawing a line parallel to ab^ fhew the bevel, or the protradtor will fhew what angle it is under. Laftly, Proceed to the circular end of the room, with its windows; and in order to find the center of the arch rop, draw pv at its foot, and parallel with ad. On the middle of pv raife a perpendicular, and continue it to / at plea- fure. Draw then the chord op, and bifed it as at n, whence raife a perpen- dicular, cutting 0/ in /. which will be the center. From the opening of each window draw the feveral radii, as (hewn in the figure, by which it will be eafily feen how much the jambs vary from thefe central lines. K a The ( 76 ) The room being thus lined out, take a ftieet of paper, and lay down a fcale of feet and inches that will comprehend the longefl: part of the room. Mea- fore then, with your common rule, the fides and ends of the parallelogram which was chalked out on the floor, and whatever thefe meafure by the rule, take the lame number of feet, inches, and parts, from the fcale, and draw the parallelogram on the paper in the fame manner as was done on the floor: and in this way go on, taking off every dimenfion from the floor by the rule, and transferring them to the paper by the fcale; fo that at length the paper will have all the lines and (hapes which the room has, by which means it is evident that the moft exad meafurement will be obtained. The next thing to be done, is to provide a place large enough to lay down the full fize of the room again. The order will now be reverfed; for thofe meafurements which were before taken from the room by a rule, and transferred by the fcale on the paper, muft again be taken from the paper by the fame fcale, and replaced on fome convenient place, by the fame rule that was ufed in taking the plan. If this method be purfued with accuracy, I ara certain it cannot fail to anfwer the purpofe, if a proper allowance be made for {training the carpet. Prob. XXVIII. Fig. 32. Plate V. To mitre any thing of the nature of a Comb Tray, the breadth of whofe fides (hall be given, and their inclination from a perpendicular predeter- mined. Let Ba he confidered equal to the given proje£tion of the fide of the tray, and let the perpendicular e a he the height of the fpring of its fides. Draw the bevel line elf, and fixing one foot of the compafles at ^, dcfcribe the arch eJ; then will d'on the bafe line be the mitre point of the fide of the tray //, and dl> will be the required breadth of its fides neceflTary to raife it to e, perpen- dicular over fl, the point of projedion. Again, if the tray fide Ihould be re- quired .r'K /}/.:). 3fifrin>/ ^■TfbrA-in(^ J/(>///(Ym^s . <f f • 1' tfhfr^cUon- deZT J Cooke ^ci<Jp '" J*ubfaj thc^ct dtreett.J\^oi'ViZij^ fy' tr Terry . ^ 71 ) quired to be raifed from its bafe up to ;«, then draw mb, which will be the breadth of the fide, and with bm in your compaffes defcribe the arch ;;; n ; then will « be the mitre point of the fide of the tray, as required. How much (horter the point n is than a full mitre, is feen from « to o of the dotted lines meeting together. Whence it is evident, that as the tray fides are raifed higher and ftill higher from their bafe, the mitres will become proportionably (horter, till at length the fides will be in an upright pofition, and confequently will have no mitre in their breadth, it will be all in their thicknefs. On the other hand, if the fides of the tray be deprefled nearer to their bafe, and ftill nearer, their mitres will proportionably increafe, until they arrive at full length, and confequently they will be in a perfedt horizontal pofition, or parallel to their bafe, and will have no mitre in their thicknefs. How to JinJ the Mitre in the Thicknefs of the Stuff. See Plate A. Fig. D. Take the fide of the tray Ob, and with it defcribe a femicircle. Make ae equal to the perpendicular height of the fide of the tray. Draw a line from e to the center; and parallel to this, fet off a line for the thicknefs of the tray fides, and the bevel of the under edge will be at 4. Draw a fquare at the center, the length of whofe fides (hall be equal to the thicknefs of the tray fides, as 3, 1 , 2. Next draw the line B A E parallel to the diameter ; and take ae^ the fine of the angle of the tray fides, and transfer it to E A. From A draw a line to the center, cutting the fmall fquare at i, and the fpace 1 .2 will be the mitre fought for ; that is, when the fides are mitred in their breadth, accord- ing to Fig. 32, Plate V, fet a gage to 1.2, and run the gage on the infide along the mitre, and plane it off to the gage from the outfide, and the mitres will all come exadlly together. If the tray fides were raifed to b, bi would then be the fine of their angle; and which being transferred from E to B, a line from B to the center cuts the fquare at 3; then is the fpace 3.2 the length of the mitre fought. And thus it is evident, that as b advances to E the perpendi- cular, fo will the mitre point B approach to D the full mitre. It is alfo evi- dent, that by this figure the mitre of any thing not exceeding in its thicknefs the diameter ( 78 ) diameter E of the femicircle may be found. For inftance, if the fides of any tray be half an inch thick, and it is required to be mitred and keyed together^ draw a fquare of that dimenfion, as the fec'ond fhevvn in the center; and if the fides bevel in an angle equal to the line e O, then 1.2 of the fecond fquare will be the length of the mitre, I proved the truth of this theory by practice, and therefore the workman may depend on its infallibility ; but he may eafily make the fame experiment himfelf. Prob. XXIX. Plate A. Fig. F. To mitre the fides of any thing of the nature of a Comb Tray, when the fides are not at right angles to each other, or when they fpring from any kind of polygon. Let the lines BO, OP, denote the fide of the polygon, or the angle which the tray fides make with each other. From O raife a perpendicular at pleafure. Confider next how much the fides are to fpring out, as from O to 4. Through 4 draw the line 4.3 parallel to OP; and next determine how much the fides are to rife from the plan, as 4.5. From 5 draw 5 O, which line gives the breadth of the fides. Turn an arch from 5 to 6, and through 6 and 8 draw lines parallel to B O, OP; which will then be the tray fides, meeting at Q^he full mitre point, provided the fides were flat on the plan. But the fides arc to be raifed till the point Q^ comes perpendicular over 2; therefore raife a per- pendicular from 2, which will cut at the point 7; then a line from 7 to O will be the true mitre for each fide. Laftly, confider the thicknefs of the tray fides, as at qs, which is parallel to O 5. From q draw a line parallel to OP, cutting the full mitre line at/', which gives the mitre at the ends of the tray fides. Thus, when the tray fides are bevelled off from Otoq, as they are rcprefented to be at No. 2, lay a fquare flat on the bevel edge of the fides, and draw { 79 ) draw a line acrofs, as at 1.2, No. 2j then take the length pg, and place it from 2 to 3, No. 2; which will give the true bevel of the ends. This pradice the workn:ian may depend on as perfeft in all cafes, as I have proved it by real experiment. And we would by all means advife the work- man to make the trial, both in this and the preceding problem, as moft ufeful and neceflary in many cafes, and which has never yet been publi(hed in any work. Prob. XXX. Fig. 33. Plate V. To find the Lines for working the Mouldings of a Clock Bracket, &c. when the front moulding projedls more than the ends. Operation. — Let aol>tJ be the plan of the clock bracket. From the center of ao draw the mitre lines to ^ and c/, and from the center let fall a perpen- dicular, as at f. From this perpendicular draw a profile of the cavetto and aftragal, according to the projedion intended for the ends of the bracket. From the fpring of the cavetto on the top of the necking raife a perpendicular up to the line ao; then, from the upper part of the cavetto, as from i, raife another perpendicular up to i on ao. Divide the intermediate fpace into any number of equal parts, as at i, 2, 3, 4, &c. From thefe draw perpen- diculars to the mitre line, and continue them downwards till they touch the cavetto at 2, 3, 4, &c. Laftly, draw from the utmoft projedlion of the aftragal, or necking, a perpendicular, cutting the mitre line at 5; then from 5, 4, 3, 2, I, on the cavetto draw parallels out at pleafure to No. i. Take in your ccmpaffes Jo from the plan of the bracket, and place it from dx.0 p, No. I. From p let fall a perpendicular; then from the plan, as before, take I.I and place it from i on the perpendicular line /> to i on the parallel line. Again, take the line 2.2 from the plan, and place it on the parallel line 2 to 2 at No. i, and fo of all the reft, forming fo many points, by which a profile of the front cavetto may be formed, and which will mitre in with the end C 80 ) end cavetto, if the mouldings are exadly worked to thefe profiles, and the mitres be accurately cut. How the mitres are to be cut is ealily feen by the mitre lines on the plan. In Plate II. Fig. 12, an example of the fame kind is fliewn, as it may be performed by the Seflor. Let the quadrant AD be confidered as one of the cavettoes to be mitred to- gether. Then let it be propofed that another cavetto is to mitre to the former, whofe projection fhall be equal to i.io. Proceed then to draw this cavetto by the fame diredtions as are given in page 33 for drawing an Oval; after which the cavettoes are to be worked according to thefe curves. The length of the mitre for the leafl: projefling cavetto is from 90 to 10, and that of the largefl projeding cavetto is from 10 to A, and the mitre line is 9.10. By thefe methods it is evident, that any moulding of different projeftions, and confiding of various members, may be worked, and cut fo as to mitre cxadly together. Prob. XXXI. Fig. 34. Plate V. Of working and mitring raking Mouldings. Let No. I, Fig. 34, be a level ovolo in a broken pediment. Make its pro- jeftion equal to its height. Divide the height of the ovolo into any number of equal parts, and from thefe divifions draw parallel lines, as is fhewn in the figure. Next, from 1.2, the extreme points of the ovolo, draw two parallel lines, according to the rake of the pediment defcribed below, which will of courfe increafe the height of the ovolo as 3.4. Draw then a perpendicular or a line fquare from either of the raking lines, as at No. 2. Divide this line into the fame number of equal parts, and from thefe divifions drav/ lines parallel to the raking ( 8i ; raking part, and continue them out at pleafure. Take then 5.5 from No. i, and transfer this opening of the compaffes to ^.^ on No. 2, and alio at No. 3, marking where it extends to. Again, take in your compaffes 4.4, from No. i, and transfer this alfo to 4.4 on No. 2 and 3, marking it as before ; proceeding in the fame manner with the reft ; by which points will be found to enable us to draw the raking ovolo fo that it will mitre with the level one at No. i, and alfo the returning ovolo at No. 3^ thus found, will mitre in with the raking moulding No. 2. In the fame manner may be found the raking and returning cyma-re6la mouldings, defcribed in Fig. ^5^ which it is unneceflary to fay any thing about, after what has been faid on the ovolo. Prob. XXXII. Fig. 36. Plate V. As I have in this Section defcribed the methods of drawlngf and mltrinsr mouldings of different proje£lions, and alfo of drawing and mitring raking with level mouldings, it may be proper here to defcribe the proportion of the Tuf- can raking Pediment, and the manner of drawing it. It, is true, according to an orderly arrangement, the Pediment fhould come after the column ; but. this is of fmall confequence, if it can as well be under*- flood in this place. The intention of a clofe pediment; whether raking or circular, is not only to ornament the front door or entrance of any building, but likewife to fhelter fuch as feek admittance from inclement weather. For this purpofe the raking clofe pediment of any order is beft calculated ; for whilft we are Sheltered from rain or fnow. by the bold projedlions of the feveral members of each order, ef- pccially the Doric, the defcending fliowers eafily and quickly glide off on each fide, on account of the rake of fuch pediments. ( 82 ) It is therefore improper to have open pediments of any order at the exterior entrances of buildings : and it is conlidered by architeds as improper to have clofe ones over interior entrances or door-ways, where they are only employed as ornamental. The pitch of the Tufcan pediment is the fame with the other orders, for in this refpeft they are all uniformly the fame ; but their intercolumniations, or fpaces between the pillars or pilafters, together with other particulars, vary according to the refpedive order to which they belong ; which 1 fhall mention afterwards, in treating on the Orders. To proportion and draw the Tufcan order, proceed thus : Obferve, that Fig. 36 is exadly half the pediment only; and therefore, in drawing a whole pediment, the divifions fpecified in the figure muft be laid on each way from the central line. And obferve likewife, that the frieze and architrave are not drav^'n to the cornice, becaufe they are not wanted in de- fcribing the pediment. Operation. — Lay down three diameters from the center of the pediment to the center of the flnaft, as at 1,2,3, in the figure. Divide a diameter into eight equal parts, and take three of thefe and place them each way from the center line of the fhaft, which gives the upper diameter of the column, as the figure fhews. Again, divide a diameter into four, as that diftinguifhed by the writing in the figure, and take three of thofe parts for the perpendicular height of the cornice : at this height draw a parallel line at pleafure fufficient for the whole length of the pediment, as the upper line with the numbers. Then take the perpendicular height of the cornice, and place it from the out- fide line of the fhaft on the line continued out from the under ed^e of the cornice, which will determine its projedlion, as is eafily feea by the level fcale line ^. Raife a perpendicular line from the whole projeftion, as g, till it cut the upper parallel line ; then will this line ferve as a fcale for the heights of each member in the cornice, the proportions of which are eafily feen by the 8 al quot ( 83 ) aliquot parts on the fcales; but if not rightly uuderftood, the reader may fufpend his judgment till the Tufcan order is defcribed. Divide the upper parallel line, which is equal to one half of the whole length, into nine equal parts, and give four of thefe for the pitch of the pedi- ment, as the figures i, 2, 3, 4, (hew. Draw then a right line from 4 to the utmoft proje(flion of the level cornice, and proceed to draw each member of the level cornice, as the fcale lines dire<3:. Note, The two upper lines, containing the nine divifions, reprefent the upper fillet of the level cyma-re£ta. The next thing to be done, is to proportion the members of the raking cor- nice by thofe of the level one. To do this, draw a line fquare from the pitch of the pediment, and continue it till it pafs through the level cornice. Take then the Ikew meafurement of the lower fillet of the level cyma-reda, as ab^ and transfer this to the raking cyma-reda downwards, from a \.ob. Again, take be from the level corona, and transfer it from b to c for the raking corona. Laftly, take c d, ef^ in the fame manner, and transfer them one after another for the raking mouldings, as before ; after which, draw lines through the feveral points parallel to the pitch or raking line, and the pediment will be completed for (hading, if required.. Of the Nature and Conjlru&ion of Hip and Elliptic Domes for Beds. Domes of various kinds have, for many ages pad:, been introduced into elegant and magnificent buildings, on account of their graceful efFedl and ma- jeftic appearance. I am of opinion that the notion of employing domes for the roofs of grand buildings, was firft fuggefted by the appearance of the hemifphere furrounding L 2 our. ( 84 ) our earth or horizon, forming a canopy or roof to the globe ; which if it were fo, domes had their origin from a truly fublime and magnificent idea. The ufe of domes for the tops of beds is of much later date than for build- ings ; but it is certain, whoever he was that firft employed domes for the tops of beds, muft be coufidered as a perfon of enlarged ideas, as no other top or roof for a genteel bed can equal them : therefore we fee them generally afed for flate beds, where both grandeur and boldcffeft are effcntially rcouifite. The term Dome generally implies a vaulted, arched, or fpherical roof Some derive it from domus, a houfe ; and others from the barbarous Latin doma^ a roof or open porch. When an arched roof is raifed from a fquare or oblong plan, it is called an Hip Dome, becaufe they require mitre ribs at eacli angle, uniting ia a center at top. But thofe domes which take their rile from an oval plan, are called Elliptic ; and, laltly, thofe which have au oclagon or hexagon for their plan may be ftyled Polygonal Domes. Prob. XXXni. Fig. 35. Plate VII. To conftru6t an Hip Dome. Operation. — Let A B C D be the under teller, upon which another tefter is to be fixed to receive the ribs of the dome. Draw the diagonals D B and AC, and their interfe£l:ion will be the center for the dome. Draw a right line through the center parallel to A B ; draw another line through the center at right angles with it, then will the diagonal lines be the plans of the hip ribs, and thofe at right angles to each other will be the plans for the center libs. Draw a circle from the center of the dome of about eight inches radius, as the ficTure (hews, which is intended as a ground for ornament in the center of the dome at the infide, and alfo to combine together the hip and center ribs. Proceed Ji^<y. /»/. 2. J. ii . ii "^• ^v,* J ■ — ■ . ^Itite. tj'hmxii?n dt^.^ Jiboke^a*^^ J\idfit.Tf/if.ffri/frt\tr7)i\\'jo.jjiiiiiv (r. Terrv ( ^5 ) Proceed next to confider the height of the dome as may be required. Let 7.6 at No. I be the perpendicular height of it, and let mn be the width of the dome. Then draw a femi-ellipfis to pafs through the points «2 6 «. Divide half of this femi-ellipfis into as many equal parts as it may be thouo-ht neceflary to have ribs in that fpacc, which in this example is fix. Draw on thefe di- vifions perpendicular lines, as the figure fhews, and fubdivide the lall: fpace, from which raife a perpendicular as before. Proceed to No. 2, and divide half the length of the dome, as/o, into the fame number of equal parts as half the width was divided into. From the di- vifions raife perpendiculars at pleafure. Take the length of the feveral per- pendiculars from No. i, and place them on the correfponding perpendiculars at No. 2, and draw a curve line through each point ; then will the ellipfis thus produced bfe the outfide fliape of all the long ribs, the fame as No. i is of the Ihort ri':3. Laftly, proceed to No. 3, which is for the four hip ribs. Draw the dotted lines from 8, 9, 10, it, 12, at No. i, till they cut the diagonal line ^ Z* at the correfponding numbers. From thefe interfedions raife perpen- diculars at pleafure, as before. Transfer the length of each perpendicular line from either No. i or 2 to No, 3 on each perpendicular as numbered, and draw- ing a curve line through each point as before, it will produce an ellipfis for the outfide fhape of each hip rib. The next thing to be confidered, is the length required for each rib, accords ing to their diftance from each angle of the dome. A little thought will make this eafily underflood ; for if No. 3 was placed in an upright pofition, being confidered as a frame, and if the portion of the curve from « to i at No. i was placed upright to it, the two points, i in No. i and i in No. 3, would coincide, and the point 2 of No, i would coincide with 2 at No. 3, and fo of all the reft. Hence, from « to i of No. i is the length of the firft fhort rib, whofe plan is at a ; from n to 2 is the fecond (hort rib, whofe plan is at i> ; from n to 3 is the third (hort rib, its plan at c ; from « to 4 is the fourth ftiort rib, its plan at ^; and from « to 5 is the fifth fhort rib, its plan at e. The long ribs are taken from No. 2, in the fame manner ; each of which has its plan laid down at No. 3, as «, i^, f , ^, e,f, fo that I need not fay any thing more on this part of the fubjedl. For the length of the hip ribs, take from J> to ( 86 ) to 5 at No. 3, and allow three quarters of an inch for dovetailing into the cen- ter block. Prob. XXXIV. Fig. 36. Plate VII. 'To con/Jruct an JLlliptkal Dome, Operation. — Let AB, DE, be the plan of the teller, whofe infide forms a true ellipfis by the help of angle pieces framed in, which mull: be evident to every workman. The oval beinsf thus formed according to the infide length and breadth of the tefler, and the two diameters being already drawn, proceed with one quarter of the dome thus: draw the plan of the upper tefter, into which the ribs are to be fixed, as the fecond elliptic line fhews. Divide then the portion of the ellipfis between and / into as many equal parts as it is required to have ribs in one quarter of the dome, as at 0, a, -6, /,y, k^ I, tending to the center b. From thefe center lines draw parallel lines on each fide, which (hall deter- mine the thicknefs of the ribs, and at the fame time fhew how broad each rib will be required, in order to give it its proper twill fo as to fuit the ellipfis ; for here it mufl: be obferved, that every rib, excepting the one that is upon each femidiameter, muft have a winding form, both infide and outfide, in pro- portion to the length of the oval with its breadth. Determine, next, how much the dome is to rife from the tefter, which, in this example, 1 confider to be equal to half the fliort diameter ; and therefore the arch of the rib B is a quadrant of a circle drawn from the center b. This arch will lerve for two ribs, that is, B and its oppofite. Likewife from the arch B we determine the outline of every other rib thus : divide the femi- diameter ab into five and an half equal parts, and raife perpendiculars till they touch the arch B. Divide the plan of the rib ab z.t No. 2 into the fame num- ber of equal parts, and raife perpendiculars at pleafure ; to which perpendicu- Urs ( 87 ) hrs transfer the Teveral lengths of thofe at No. i to the correfponding ones at No. 2, as acdefg ; by which the rib A will be formed. The libs for h'lj and k are formed in the fame manner, and therefore it is unneceflary to defcribe thefe. Obferve ; C, on the plan of the elliptic tefter, is for the long center rib and its oppofite, as will eafily be uuderftood by infpefting the figures, and a little refledion on the fubjeft. Of the Management of Elliptical Domes. Thefe domes may be made in four parts, the fame as hip domes, if required. The ribs of thefe domes are all dovetailed into a center block, which may be circular or elliptical to fuit the dome, and which ferves for the ground of a carved and gilt patera for the infide of the dome, as has already been mentioned on hip domes. When the ribs are all completely fixed, the fpaces between them may be filled up by gluing white deal in ; and when the pieces of deal are worked down to the ribs, the whole will form an agreeable dome, which fhould be covered with canvafs, and painted to fuit the furniture, or otherwife covered with the fame kind of fluff. And if fo, it will be unneceflary to cover it witji canvafs ; but as the fluff mufl be put on the dome in fo many breadths, cut fo as to anfwer its fhape, a gimp may be flitched on to hide the tacks and give the dome a more rich appearance. But if the dome be large, it may have fmall gilt moulding in place of the gimp, which are fixed to the dome by gilt-headed fcrews. For the infide of the dome, it will be requifite to have a gilt moulding, to hide the joining of the under and upper tefter, and to fcrve as an architrave to the dome. The ( S8 ) The triangular compartments at each corner of the tefter, occafioned by the manner of framing it to fuit the dome, fhould have fmall mouldings put on to fuit that fhape, which will take off the flat and heavy appearance it would otherwife have, and add to the effedt of the whole. As for any other particu- lar with refpeft to ornaments, what has already been obferved on hip domes, may alfo be applied here. With refpect to the dome defcribed by Fig. 37, I do not think it neceflary to go through an explanation of it after what has been faid on Fig. 35, which, if the reader has fully underftood, he cannot fail to be acquainted with the lines laid 'Ijwn in Fig. 37, merely from infpedion, efpecially as I have marked each, correfponding line with fimilar letters and numbers. ( S9 ) SECT. VII. Of the Proportion of the Jive Orders, adjufiedhy Modules, Minutes, and aliquot Parts; together with Jome Account of their Antiquity and Origin. Aljo of the general Proportions of Frontifpieces adapted to each Order. INTRODUCTION. I HAVE no doubt but it may be thought unneceffary by feme to introduce the orders of architedture into this work, after fo many publications of this Ibrt by men of the firft clafs in the profeffion of the art. To remove this obje£lion and unfavourable impreflion from the mind, I fhall juft mention two or three particulars which induced me to make the five orders a part of this Drav^'ing-Book. Firft. — In my opinion, and it is prefumed that I am not fingular in this, nothing can appear more worthy of a place in a complete drawing-book than the five orders accurately laid down and neatly engraved ; by which we fee the proportions and etFe6l of each moulding arranged and connected together, according to the compofitions of thofe ancient architedls of Greece and Rome, who are lo juftly famous in the world. Befides ; from a plate of the above kind, we are not only made acquainted with the proportions and fliape of each moulding, but have likewife the ad- vantage of feeing the effeft of light and fhadow produced by the fun's rays falling in a certain diredlion on the feveral parts of a column. M The ( 90 ) The knowledge of thefe particulars mufl: ever be confidered as efTential parts of <^ooJ drawinsf, in which architedure is often introduced, and ibmetimes makes the principal figure. Second. — As many cabinet-makers, and even fome ingenious upholfterers, are found defirous of having a knowledge of the five orders, and the propor- tions of the feveral frontifpieces, I thought an attempt of this Ibrt would be favourably received, as it undoubtedly tends to make the work more generally ufeful, and will prevent the trouble and expence of having recourfe to other books on the fubjeft. And this has not been merely my o-.vn opinion, but the fentiment of fome well-wiflicrs, who defired me to let the orders have a place in my book. Laftly. — Befides the reafons juft mentioiied for publifhing the five orders, I muft frankly own mylclf a lover and admirer of thofe ancient produ(5lions of ingenuity and art, which, in c»y opinion, cannot be much, if In the lead, im.- proved by the force of modern genius. If, therefore, the author confiders himfelf as a kind of devotee or bigot to thefe remaining monuments of ancient ingenuity, furely he may be granted the liberty of paying the following fmall tribute to the memory of thofe great architedls who had the honour of bringing the five orders to that perfe(5tion which we now fee them in at this day. And further, as I believe that the orders are now brought to fuch perfedion in their proportions, as will bear the ftriileft mathematical examination, I confider them as incapable of improvement, except perhaps in fome part of their ornament, and therefore they are clafled with thofe things in this book that will remain unalterable. Of ( 9^ ) Df the Origin and Antiquity vf the Orders of Architeflure. Some diftindion is to be regarded between the origin and antiquity of the orders, and that of archite<Slure * in general. The firft ideas of archite£ture in general, may perhaps be traced from thofe de and irregula: bitations of man. rude and irregular methods of building tents and huts which were the f.rfl ha- But in thefe fl:ru£tures, nature and neceffity were their only guides, unlefs they obtained fome infl:ru£lions or hints from the manner in which birds build their nefts-, as Vitruvius conjedures. We are informed by Mofes, that Jabal was the father of fuch as dwelt in tents : and I fuppofe it is meant, that he was the firfl maker of them likewife. And I further imagine, that the city which Enoch built about that time was an affemblage of thofe tents, perhaps furrounded by a mud wall, and fo ob- tained the name of a city in thofe days; for it can fcarcely be thought that they had at that time either difcovered ftone, or knew how to make brick, and much lefs how to put them together in houfes, io as to form a city accord- ing to thofe mentioned in after times. But, however, very early after the flood of Noah, we read of an attempt made to build a city and tower whofe top was to reach the heavens ; meaning to be a very high one. Their materials were then brick, and flime for mor- tar. And when we confider how great their defign was, and how fuccefsfully they proceeded until the Divine Hand ftopt them, we mufi: neceflarily infer. * Architecture implies the fcience of building in general, which gives rules for defigning and laifing all kinds of ftruftures or edifices. It is from the word architect:, compounded of aex^f » crchos, the principle ; and tty%y, teiion, the chief artificer, or one who gives rules for, and dire6U the ma- nagement of, buildings. M a that ( 9:^ ) that men in thcfc: days began to know the rules of building, and of courfe this may be confidered the origin of regular architefture *. But the origin of that part of architefture called theyfx;^ Orders, is of much later date than this. They appear to me, and it has been the opinion of fome great architeds, that they owe their beginning to Solomon's Temple. I do not mean that pillars or columns were never in ufe before this famous building was ere6ted, but only that we do not read of certain proportions af- figned to their height and diameter till thofe given to Jachin and Boaz, the names of two pillars fet up at the entrance of the porch of this building. We read of pillars above four hundred years before the days of Solomon : and we read alfo, that thefe pillars had chapiters and fillets of gold and filver ; but no mention is made of their height + or diameter ; yet fomething may be known as to the intercolumniation of thefe pillars, for there were twenty pil- lars {landing in an hundred cubits, the length of each fide of the tabernacle. See Excd. xxxvi. 38. and xxxviii. 11. However, as there are no proportions afligned to thefe pillars, I prefume we cannot date the origin of the orders here ; yet I think there would be more plaufibility in it than what fome have advanced on this fubjedl. * This tower was 660 feet high at the time of the confufion of tongues ; and from the proportion of its bafe, which was not quite fo large as the Egyptian pyramids before mentioned, fee p. 60, it may be prcfumed that they did not intend literally to make the tower reach to heaven, even according to their own conception of that place, otherwife they muft have affumed a more extenfive bafe or area for that purpofe. It is probable, therefore, that this prodigious building was brought to a finifli at this height. Profane hillory informs us, that it benched in from the bottom to the top in a fpiral form, and the platforms occafioned by the benching ferved as a ftaircafe, which was fufficiently broad forhorfes and carts to turn upon it. The fpaces between each benching was 75 feet high, and con- tained manv ftately rooms, with arched roofs ; which is a further proof of their (kill in architefture. And \vhen it is confidered that their bricks were 18 feet long, 14 wide, and 7^ thick, th.-y muft have pofleff^d fome knowledge of the meclianic powers, in order to move fuch ponderous ftones and raife them fo high. About this tower was afterwards built the great city Babylon, the glory of the Chaldeans. t Jofephus indeed fays, " Every pillar was five cubits in heiglit ;" and he fpeaks alfo of five pillars at the entrance of the tabernacle^ that were gilded, and Hood 011 bafes of bi afs. I The ( 93 ) The pillars which Solomon eredled at the entrance of the temple were of the following proportion, according to the language of the fcriptores ; — Their height was eighteen cubits, or twenty-feven feet without their chapiters or capitals; and their chapiters were five cubits; which in all makes thirty-four and an half feet in height. A line of twelve cubits did compafs either of them, about, confequently their diameter was fix feet; and had thefe pillars been one cubit higher, their proportion would have anfwered exaftly to the original: Doric * Order,, whole height was equal to fix of its diameters.. Befides the likenefs or affinity between the Doric column and thofe fet up. by Solomon,, will ftill appear more ftriking, if we. confider that the ancient Doric had no plinth or bafe ; for there does not appear to have been any at the foot cf Jachin and Boaz, otherwife I think they would have been, mentioned as well as the chapiters. But thefe columns are faid to have fillets, whofe thick- nefs was four fingers, and they were made hollow. See Jer. Hi. 21. Thefe fillets feem to anfwer well enough to the Doric necking at the top of the fhaft. They were hollow, and of four fingers thlcknefs or projedlion, which Is nearly the fame projeftlon as would be required in the necking of a Doric column of the dimenfion of Jachin and Boaz. There is another particular that may be mentioned which alfo bears fome likenefs to the Doric, and that is the fize of the porch or entrance, on each, fide of which thefe maffy pillars were placed. This opening was twenty cubits in width, and forty in height, anfwering, to the proportion of the Doric frontlfplece or door. And laftly. — The lily-work on the chapiters, and the rows of pomegranates round about the chapiters, were, in my opinion, as likely to have given * For fome time after the firft invention of this order, the proportion of its diameter to the height was as the length of a man's foot is to the height of his whole body, which at that time w:.s reckoned to be oae fixth part ; but afterwards they added another diameter, and at length brought it to eight. rife ( 94 ) life to the ancient Doric order, and more fo than the manner of building an- cient huts, by placing trunks of trees on each fide, by which the roof was fupported. Yet I will not fay but trunks of trees thus employed, might firfl: give ex- igence to the notion of fome kind of a pillar to be ufed in the firft buildings of brick or ftone, while, at the fame time, I am inclined to think that columns were never reduced to any order till the building of Solomon's temple by God's appointment. However it is not to be underftood as if the regular Doric order could be exaftly copied from Solomon's pillars, but only fuch hints and propor- tions taken from them as ferved in after times to compofe the firfl order of architefture. Nor can it be thought that the firfl compofition of the Doric column had thefe triglyphs and mutules which we now fee it has, till after it was reduced to its proper form and chara£ler. It is therefore thought to have been more fimple and maffy in its primitive flate ; fomething like the Tufcan order. Some imagine, and not without ground, that the Tufcan, nearly as we have it now, was the firfl flate of the Doric, Vrtruvius fpeaks of a flate in which the Doric column was in before it was reduced to order ; for, treating of the antiquity of the Doric, that it was ufed in the temple of Juno, at Argos, he fays, that, " the fame order was alfo ufed in the other cities of Achaia, before the laws of its fymmetry were eflablifhed.^' This indicates that it was in a more rude flate before it was employed in that famous temple. But if that temple, dedicated to Juno, was erefled in the days of Do- rus, the king of Argos, as Vitruvius intimates, it would be rather incredible to think that the Doric order fhould be in exiflence in times fo long before 2 Solomon : ] ( 95 ) Solomon * : and, upon fiich a fuppofitlon, thofe who maintain that the firft idea of the orders was derived fron:i Solomon's temple, would be grofsly mif- taken. A certain author, after quoting Vitruvlus on the fubjeft, fays, " Such is the account given by Vitruvius of the origin of improvements in the propor- tion of columns. Had improvements, however, exilled in fuch early times, Homer t, who was greatly pofterior to them, would certainly have made mention of fomething of the kind ; but in all his writings he gives us no account of any thing like columns of jftone, but ufes a word which would rather incline us to think, that his columns were nothing more than bare poflsJ* This account looks as if there had been neither ftone columns nor temples till after Homer's days. For if the architefture among the Greeks in thole days coniilled in bare pofts, we cannot fuppofe that thofe temples which they dedicated to their gods were compofed of columns of marble, of other ftone, otherwife he would not have left them unnoticed. It would rather feem as if the Greeks had borrowed their frft notions of temples to worfhip their gods in, and alfo their architedture to adorn them with,^ from that at Jerufalem. Agreeable to this view, the above quoted author fays : " It is remarkable that improvements in archlte£hire did not take place in any nation till after, or about,, the time that Jerufalem was taken by Nebuchadnezzar. The grandeft buildings amongft the Aflyrians feem to have owed their exiftence to this monarch ; and it can fcarcely be imagined that he would not endeavour to imitate the archite£lure of Solomon's temple, to which, by his conqueft of Jerufalem,. he had full accefs J." * Dorus rmifl: have been, at lead, four hundred years before Solomon, if he reigned at Argos before the expedition of the Argonauts. + Homer was born above nine hundred years before the Chriftian aera. I According to Prideaux, Nebuchadnezzar took Jerufalem fix hundred and five years bcfwe Chrift. Upon ( 96 ) Upon the whole then, I thiak it will agree better to the above fads, if we affirm that the Doric order had its name and improvements from the Dorians, who occupied the country of Doris, a Grecian diftrift, of which Dorus had ■formerly been king. The Ionic order fucceeded the Doric, according to antiquity, and was ?n improvement from it. It had its name from Ion, the Grecian country or diftridt where it was invented, and firft employed in the temple of Diana at Ephefus. By the accounts we have of this temple, archite6i;ure muft have arrived to a coufiderable degrfee of perfection in theie times. This temple at Ephefus, the metropolis of Ion, was about four hundred and forty feet long, and two hundred and thirty feet wide; was fupported by one hundred and twentv-feven pillars of the above order, apd about fi:ity-two feet high. It was built in marble, and decorated with the finell ornaments j and, as the biflory fays, exhibited the moll perfect model of this order. The Corinthian comes next in order, which has its name from Co inth, a city or chief town in Achaia, a Grecian diftrid or territory. In this city the Corinthian order had its origin. The account which Vitru- vius* gives of it is fbmewhat curious and entertaining ; 1 (hall therefore tran- fcribe it. ■" The third," fays he, '^ which is called Corinthian, is in imitation of the delicacy of vireins ; for the limbs are formed more flender, and are more grace- ful in attire. The capital is reported to have been thus invented : — a Co- rinthian maid, being feized with a diforder, died ; after her interment, her nurfe collected, and difpofed m a balket, the toys which pleafed her when alive, carried it to the tomb, placed it on ihe top, and, that it might endure the lon"^er in the open air, covered it with a tile. The balket chanced to be iplaced over the root of an acanthus, which being thus deprefled in the middle, * ^'itruvius was an ancient Roman arclilrcfl, who wrote a fyflem of archltedure, it is thought, in the time of Titus, the eleventh Roman emperor, who reigned in the year 79, to whom he dedi- cates the woi'k. the ( 91 ) the leaves and flalks iu the fpring feafoii iflued outward, and grew round the fides of the balket ; and being prefTed by the weight at the angles of the tile, were naade to convolve at the extremities, like volutes. At that time Calli- machus, who, for his ingenuity and excellence in the arts, was by the Athe- nians named Catatechnos *, happening to pafs by this tomb, took notice of the bafket, and being pleafed with the delicacy of the foliage growing around it, as well as the novelty of the form, made fome columns near Corinth ac- cording to this model, and from thence eftablifhed the fymmetry, and deter- mined the proportions, of the Corinthian order." The Tufcan order is the fourth in point of antiquity, but in the arrange- ment of the five orders it is put firft, on account of its fimplicity and plain- nefs. It had its origin in Tufcany, a place remarkable in Italy, which was firft inhabited by the ancient Lydians out of Alia. Thefe people firft built temples of this order, and dedicated thent\ to their gods in their new planta- tions. Vitruvius calls it the ruftic order, which is confiftent enough with what I formerly conjedured, namely, that this order was the firft ftate of the Doric column in its moft antique form. And the circumftance of its being brought from Afia by the ancient Lydians, helps to confirm it. The Compofite is the laft. Its name denotes that it was compofed from the other regular orders. 'O' It is alfo called the Roman order, becaufe it was reduced to its proportional ftandard in that country. It does not appear to be fo ancient as the days of Vitruvius, as he makes no mention of it. He fpeaks of various capitals that might be introduced on the Corinthian column, but does not name them. *' There are," fays he, " alfo other kinds of capitals, called by various names, which are difpofed on the fame columns, and which have no proper fynimetry or relation to any order of co- lumns that can be named differently ; but they' are all derived and transferred from the Corinthian f." * The firft of artifts. f See Newton's Tianflation of Vitruvius. N Thefe ( 98 ) Thefe words, and the liberty they convey in favour of the compofirion of varieties of capitals to the Corinthian column, it may be prelumed, gave rife to the compofitiou of this order, which, in any other refpedt but the capital, is nearly the fame with the Corinthian. Some architects, however, do not incline to fpeak well of it, becaufe it appears to have been picked and culled from all the other orders, and is fometimes badly arranged, on ac- count of the liberty both taken and granted in this fpecies of architecSliire. However, in my opinion, it forms a very beautiful appearance when rightly managed. The original inventor of the compofite order is thought to have been one Serlio. Having now faid as much on the antiquity and origin of the five orders, as is neceflary to give a workman a proper view of the fubje£l, I (hall now pro- ceed to defcribe the proportions and charadler of each diftindt order, and like- wife explain the names of each moulding. Of the Tufcan Order. See Plate VIIL The Tufcan order is the moft fimple of any of the orders. It is alfo diftin- guifliable from the other, on account of its ftrong and maffive appearance. On which account, in the figurative flyle, it has obtained the name of the ruftic order ; and in conformity to this charader it is generally employed in farm- houfes, ftables, and other buildings in the like fituations. It is, however, fometimes ufed in grander buildings, where ornaments are not required, but where ftrength is the principal objed. The proportion of the Tufcan column, with its pedeftal and entablature, is as follows : Divide i 99 ) Divide the whole height, for the complete column, into five, as the figure fliews. Take one of thefe parts for the pedeftal as at i, whence the line is di- reded that determines the height of the pedeftal. From this line divide the whole height again into five equal parts, as the fecond upright fcale (hews. Take one of thefe parts for the whole entablature, and the remaining four is the height of the column, including its bafe and capital. Divide the height affigned for the column into feven equal parts, as is (hewn on the third up- right fcale. Take one of thofe feven parts for the inferior or lower diameter of the column, not including the projeftions of the bafe, but fimply confined to what is commonly called the (liaft, or cylindrical part of the column. Take half of the inferior diameter, and give it for the height of the bafe, and alfo for the height of the capital, not including the aftragal at the neck. Proceed next to draw a module, by which to determine the fmaller parts of the column, with the heights and proje<5tions of its members, as fpecified by the upright and horizontal numbers oppofite to each member on the large fcale. Draw a right line at pleafure. Lay on this line a fpace equal to one di- . ameter. Divide it into fix equal parts, and draw perpendiculars from each divifion indefinitely. Lay on five equal divifions on any of the perpendicular lines, and draw parallels through each. Draw then two oblique lines, meeting in a point at halfof thefirft divifion 10, which fpace will then be divided into ten, at the numbers i, 2, 3, 4, 5, &c. fo that any number of minutes up to fixty may be accurately taken from this fcale. I have alfo (hewn a module at the bottom of the larger pedeflal, which is equal to two of the fmall modules, from which all the minutes are taken and placed as before mentioned, as the Plate of itfelf will make fufficiently clear by infpedion. A module is confidered by fome as only half a diameter, but others extend it to a whole diameter ; which lafl: I have adopted, as being the mofl: fimple and entire, and therefore more eafily remembered by workmen. N 2 Vitruvius ( I<^ ) Vitruvius ufes the large module, reckoning the proportions of the column by the thicknefs of the lower diameter of its fhaft. And I do not fee but it anfwers as nearly to the different parts of a column as the femidiameter does, or as that of twenty minutes, which has been contrived by fome. The projection of each member is alfo denoted by aliquot, or equal parts ; and each part is equal to a minute taken from the fcale : fo that if the reader fhould find any little inaccuracies in the aliquot parts, which it is almoft im- poffible to avoid in fuch fmall fcales, he may corredl thefe by the whole num- ber. And obferve, that the cornice of the pedeftal projedts iij minutes, which is- the whole fum of the projection of each member, denoted by 2, 4, 2, 2i, and which amount to 11^. The bafe of the pedeftal proje(5\s the fame. Its fillet is two parts ; the ogee, or cyma-reda, feven and an half; and the fquare two ; which is in all eleven and an half. The bafe of the column pro- jedts ten; the conge, or apophyge, four; and the torus fix. The upper conge of the neck of the capital three, and its aftragal one and an half. The capital, in all, projedts twelve minutes ; the firft fillet two, the ovalo (eveUy the abacuo one before it, and the upper fillet two. The whole projc6lion of the architrave is five, the upper facia one and an half, and its fillet proje(fts three and an half. The whole cornice projeds forty-five minutes, and its height is equal to its projection. Of the Diminution of Columns. Some diminifh columns by a right line drawn from the inferior to the fu- perior diameter ; but this is very jejune and infipid, becaufe when columns are finifhed ftridly in thTs mode, they appear too flender in the middle, and lole that graceful effect which an ea(y curve line produces. It appears that fome of the ancients dirniniflied the fhafts of their columns by a curve hue one third from the bafe, as in Plate Vlll. whilft others of them carried this point to an extreme, by drawing a regular curve line from the ( 10, ) the inferior to the fuperior diameter, producing a diameter In the middle of the fhaft larger than that at the bottom. This notion has been charged upon Vi- truvius, becaufe he fpeaks of " an augmentation that fliould be made in the middle of columns;" but Mr.Newton, in a note in his book of Vitruvius, has cleared him of this charge. See page 53. And Sir William Chambers takes notice of an author who fuppofes the " addition mentioned by Vi- truvius to <i2;nifv nothing^ but the increafe towards the middle of the co- lumn, occafioned by changing the flraight line which at firft * was in ufe, for a curve." *' This fuppofition," fays Sir William, " is extremely juft, and founded on what is obferved in the works of antiquity; where there is no inftance of columns thicker in the middle than at the bottom, though all have the fwelling hinted at by Vitruvius, all of them being terminated by curves." The method that this gentleman recommends as mofl; proper for diminifh- ing columns, is by an inftrument which Nicomedes invented to defcribe the firlt conchoid ; for this, being applied at the bottom of the fhaft, performs at once both the fwelling and the diminution ; giving fuch a graceful form to the column, that it is univerfally allowed to be the moft perfe£l pradice hitherto difcovered. This method has been adopted in the diminution of the Ionic, Compofite, and Corinthian columns in Plate X, XI, and XII ; becaufe thefe are the moft delicate orders. But, in the Tufcan and Doric (hafts, I have followed the common method ; becaufe thefe robuft columns will admit of more apparent, or more fudden, diminution than the other three. The moft common method is as follows. See Plate VIII. * This means, before the orders of architedlure had received much improvement. Divide ( I0» ) Divide the fliaft into three equal parts, and draw a diameter at the firfl: part. On this diameter defcribe a femicircle, and divide the femidiameter into five equal parts. From the fourth divifion raife a perpendicular line which deter- mines the upper diameter and cuts off a portion of the femicircle, which is to be divided into four on the curve. Laftly, divide the upper two thirds of the fhaft into four equal parts, anfwerablc to the four equal parts on the curve ; and from each of thefe divifions, or parts, on the curve, draw right lines to the correfponding divifions on the fhaft, by which four points will be found through which the diminishing curve line is to pafs, and, if accurately drawn, will appear Imooth. Obferve, this diminution brings the column, at its fuperior diameter, to forty-eight minutes ; but in all the other orders there are uniformly fifty minutes allowed. Some architedts, however, contend for various degrees of diminution, ac- cording to the charadler of each column. They aflign to the Tufcan one fourth, to the Doric one fifth, to the Ionic one fixth, to the Compofite and Corinthian one feventh, of the inferior or largeft diameter. This makes no difference, however, in the method of diminution above taught ; for if the Tufcan be diminished one fourth, then divide a femidiameter into four parts, and take one of thofe for the diminution on each fide, and proceed as before ; fo alfo of the other. I (hall now quote a few words from Sir William Chambers on this fubjeft, by which the reader, if he pleafe, may form his judgment. He fays, " In the remains of antiquity, the quantity of diminution is various ; but feldom lefa than one eighth of the inferior diameter of the column, nor more than one fixth of it. The laft of thefe is by Vitruvius efteemed the moft perfeft. Vignola has employed it in four of his orders, as I have done in all of them, there being no reafon for diminishing the Tufcan column more in proportion to its diameter than any of the reft." How JYrjti- a'. T. SA^nUen Al^ . T^Npud tu l^ Acf din4^i^. ^t- T^hem&n 7?^c/' <^./7^/ yi^--**. 'i.*^ ( »03 ) Hoiv to dimlniPo any Column, from the inferior to the fuperior 'Diameter^ by means of an Eiliptic Curve not exceeding in its S^vell the inferior Diameter, Fig. I. Plate XIII. is Vignola's method of dimlnifhing a column, the prin- ciples of which 1 have taken from Sir William Chambers' Treatife on Archi- tedlure, but have here defcribed it in my own way, as follows. Determine the height of the fliaft as at c d, and draw a line for its axis. Next, draw ^ a at pleafure, and at right angles with the axis. Let b c h& half the inferior, and n d half the fuperior diameter. Take b c, half the under dia- meter, and with the compafles place it from n, the extreme point of the upper diameter, to any point where it falls on the axis of the column^ as at o-. From n draw a line through o, and proceed till it cut the bafe line ba zt a. Draw a line at pleafure from b, the extreme point of the inferior diameter, parallel with c d ; and divide this line into a number of equal parts, as 2, 4, 6, 8, &c. From a, the center, draw a ray or right line to each of thefe divifions, which will pafs obliquely through the axis, in proportion to their diftance from the inferior diameter be. Take then b c, half the diameter, and place it from I to 2, from 3 to 4, and fo on of all the reft. Laftly, through each of thefe points draw a curve line, and the diminution of one fide of the column will be thus completed, as is (hewn by the dotted line on the right hand. To deter- mine the other fide of the (haft, nothing is wanted but to draw a fquare line acrofs the fhaft from each point, and place the diftance2 a: to xy, and / 4 to / 9, and fo on of the reft. Fig. 2 is Nicomedes' inftrument, which, as it is here defcribed, is intended to perform the fame diminution as has been above explained by lines. This inftrument is made in the manner of a fquare, with a ftay to keep it firm, as at R ; ;^^ is a dovetail groove cut in the center of the upright piece, as T ; bah its bafe, in which alfo there is a dovetail groove as at « ; / w is a ruler, ( I04 ) ruler, or trammel, which moves by the dovetail-piece Y in the groove bp, by which the diminution is performed; glj is a plain groove cut through the trammel, and ^ is a center pin which guides the trammel as /' pafles from p to b ; when / is at by it is evident that h will be at g the center pin, becaufe hi is equal gb ; alfo^/ is equal oa in Fig. i. and found in the fame manner. The interval, or fpace, between the center / and k at the end of the trammel, is equal to the inferior diameter b m^ or bc^ Fig. i. As, therefore, the cen- ter / paffes to by the center k, in which a pencil is fixed, cuts all the oblique linesyy tending to ^, in the fame points as at 2, 4, 6, 8, &c. of Fig. i. and at the fame time draws a perfedl curve ; at leafl it is fo when the center is not nearer to b, the bafe of the column, than g is ; and it cannot be nearer, ac- cording to the quantity of the diminution always affigned by archite6ls; but if g be moved towards the bafe ^, in proportion thereto the curve at the top will become too ftraight. This, however, is no reafonable objedion to the ufe of this inftrument when applied to columns ; for certainly it muft ever be con- fidered an advantage to be able to draw a curve by an inftrument, which other- wife muft be drawn by the hand through certain points, which it is not ea(y to do in the whole length of a column ; and, though it be not abfolutely per- fedt when ufed for any thing that requires much more diminution than a co- lumn, yet we affirm it to be without defedl in that cafe, and to exceed ar)y other method yet publilhed. Laftly, in order to make this inftrument anfwer for fliafts of various fizes, the plain groove g h muft be lengthened each way to v and w at pleafure. The upright pb^ and the bafe piece N a, muft alfo be proportionably lengthened ; and if the center pin g be fixed in a moveable piece to Aide each way in the o-roove ?/, and fixed at any certain place by a fcrew, as may be required, then it is evident that the inftrument may be fo conftrucled as to anfwer columns of any^dimenfion. Of the principal Farts of a Column^ and the Names of each Member. The principal parts of an entire order are three; the pedeftal, ftiaft, and entablature. The ( ^05 ) The pedeftal is the lowermofl: part of aa order, comprehended between y and F, fee Plate VIII. The column is the middle part of it, including the whole fpace between the pedeftal and top of the capital. The entablature is the uppermoft pr.rt of the whole, and contains every member between m, the top of the capital, and a. Thefe principal parts are again fubdivided as follows. The pedeflal con- tains the plinth F, dado B, and cornice A zy. The column includes a bale, fhaft, and capital ; and the entablature, an architrave, freeze, and cornice. Thus, in every entire order there are three principal parts, and each of thefe parts are again fubdivided into three fmaller parts, which in all make nine ; the origin of whofe names is as follows: 'O F, the plinth, is from TrXivS^oj, pUnthos, a brick, or fiat fquare ftone, on which columns, in their moft antique flate, are fuppofed to have ftood. B, the dado, or dye, fo called becaufe it is of a cubic form. A, z,y, the cornice, from the Latin coron'js, a crowning; becaufe the cor- nice is the finifhing, or crowning, of the pedeftal. X, w, V, tTie bafe of the column, from /Sao-*?, da/Is, a foundation or footing for the column. The fhaft is that long and ftraight part of a column comprehended between the bafe and capital. Some derive it from o-kxttJco, J^apto, to dig, in the manner of a well, round and deep, whofe infide refembles the fhape of a pillar ; and fome from the long part of an arrow or fhaft *". The fliaft ot a mine is the round perpendicular paffage they make to come at the ore. O ^, p, 0, ;;, w. ( ro6 ; q,p,o,n,m, the capital, from Ke(p»X-)j, kepbak; ox caput, the head, which the capital is to the column. /, k, i, the architrave, {o called hecaiife it is the chief fupport to the whole entablature, from a^^voj, an/jos, chief or prhicipal ; and the Latin tral>Sf a beam. /j, the freeze, " from (pi^povy phibron, a border or fringe ; or which the an- cients ufcd to call t^upo^oq, becaufe it was ufually enriched with the figures of animals." From J to rt is called the cornice, which is the fame to the entire order as the pedeftal cornice is to it. See A, -Zjy. Thefe fubdivifions of the entire order have each their particular members, except the dado or freeze ; and on the proper arrangement of thefe members, depends much of the beauty of the whole. The names of thefe members are as follows : a, the fillet, from the French word^/, thread. b, the cymatium, or cyma-redta, from KUfianovy kumation, a wave ; becaufe this member refembles the fwelling and concavity of a wave. f, The fillet. d, the corona, or crown ; becaufe it is a principal member of the cornice, and ferves as a (heltcr to the fmaller members of the entablature. The hollow part appearing at the under fide of the corona, is termed the drip. e, the ovolo, or Latin ovum, which means an egg ; becaufe this member. DO in ( i°7 ) III the Ionic, Compofite, and Corinthian orders, is generally carved in the fhape of eggs and darts. g, the cavetto, from the Latin cavus, hollow. /, the fillet, liftel, or fquare of the architrave. i, the upper fafcia ; and /, the lower ditto. niy the upper fillet of the capital. n, the abacus, from a^u^f abax, a fhelf or table ; or, as fome fuppofc, a tile on which the ancient Greek mathematicians flrewed dufl to draw their 2:eometrical fchemes on. This word feems to have been introduced into archite£lure on the invention of the Corinthian capital, which had its rife from an acanthus growing round a bafltet with a tile laid over it, as has already been defcribed from Vitruvius. Confequently 0, the ovolo, which is the fucceeding member, mufi: be confidered as the bafket over which this tile was placed. />, the lower fillet of the capital ; and q, the freeze of ditto. r, the aftragal, from ug^oiya.\o?, aflragalos, a bone of the heel ; or the cur- vature of the heel, which this member refembles. J, the upper cinclure, which it is thought was anciently an iron hoop, or ferule, to fecure the ends of the columns, when they were uicd without ca- pitals or bafes. O 2 /, the ( io8 ) /, the upper conge or apopKyge, from onro(pvyvi, apopbu^c, eicape ; becaufc that part of the columti appears to fly off. u, the lower ditto ; and v^ the lower cinfture. w, the torus, from tcjcj, toros, a cable, which this member refeniblcs, X, the plinth of the bafe. y, the fillet ; and z, the corona, as before. A, the cyma-reverfa, or the cymatium inverted. DE the bafe of the plinth, whofe members are named the fame as thofc' of the like (hape already defcribed. In every other column fimilar members have the fame name, and therefore I fliall not repeat them over under the other columns. But as there are fome niembers in the fucceeding orders which differ in charafter and (liape from thole that have been mentioned already, I (hall here point them out, to prevent future trouble, and to keep this part -of the fubjed of architedure to2;ether. The Doric, Plate IX. for inftance, has a fcotia marked A, from (tkotiu, /kotia, darknefs ; becaufe of the flrong fhadow which is produced by its own concavity and the projedling aftragal above it. m, the conic drops, fo called from their figure. k, the triglyphs, from r^iyXvpog, trig/up/jos, three engravings. It is a com- pound of TPi, tri, three ; and yXv^pu^ ghipbo, to carve or engrave ; in con- formity to which derivation, the triglyph has two entire channels, and two half ones, with three fpaces between. It is faid that the triglyphs peculiar to this / r'//r { //uy r Tj'keraten DeUn. t ^^^rf!//^ ■r v';;. . ' 1 La \ -:ri r * A ZZL ti It Ji iitii \ \ \-\ \ V 7 3 [^ 33/ X. ' 3ii 3 /ti ., ^/,.,/./, I'l'll'l 7 3!."» fiM/^d or tif Are dhrar. iy T-f/uratm J>tc'tf'tpfi y..i,~r„.j,^,^ ( 109 ) this order were firfl: ufed in a temple at Delphos dedicated to Apollo, becaufe his lyre was of this Ihape. e,f,g, the mntule, from the 'L.AX'm mutuli, modillion j fo that, properly fpeakine, the mutules are to the Doric the fame as the modillions are to the Compofite and Corinthian orders. In the Ionic order, Plate X. there are two members which differ from thofe already mentioned, as o the volute, and D the dentils. The volute is fo called from the Latin volvendo, to roll round, as on a ftafF*. Some call the volutes the horns of the capital, becaufe they pretty much refemble the twifting of rams horns. The dentils are from denteUl, teeth, which they refemble ; and the flat member on which thefe dentils are placed is termed dcntkulus. The Compofite capital is adorned with acanthus leaves, and the Corinthian with thofe of the olive. Of the Charadier and general Proportions of the Dork Order. See Plate IX. The chara£ler of this order is confidered by architefts as grave and robuft. Hence, in the figurative ftyle, it is termed the Herculean Order ', of which order fome temples were formerly built, and dedicated to Hercules as well as to Apollo. It is generally ufcd in large and flrong buildings, as in the gates of cities, * The term volume has the fame origin, becaufe anciently they formed books by fheets of written parchment or bark rolled round a ftick. and ( no ) and at the outfide of churches. And, as its entablature is of a very large pro- jedion, it is generally employed in fituations where ihelter is required. The whole height of the entire order is divided into five equal parts ; one of which is the height of the pedeftal. The column and entablature is divided into five alio; four of thefe parts are affigned for the height of the column, including the bafe and capital ; thefe four parts are again divided into eight equal parts, one of which is given for the inferior diameter of the fhaft. The entablature is two diameters in height, its cornice is forty-five minutes, and its projeclion is one module. The (haft fometimes is left plain, and fome- times it is fluted. The number of flutes is twenty or twenty-four, and the depth and curvature of them are determined by drawing an arch from the lummit of an equilateral triangle, whofe fides are equal to the breadth of the flutes, as at o. To diminish the flutes in proportion to the column, divide the upper two thirds of the fliaft into four, and find the femicircles i, 2, 3, 4, 5, in the fame manner as was taught in the Tufcan order. Then divide each of thefe femi- circles into ten or twelve, and draw lines from each point or flute perpen- dicular to the diameter, as 1,2, 3, 4. Take thefe fpaces on each diameter and transfer them to their correfpondent diameters on the column, which will give the diminution required at each for the flutes. Lafily, as the Doric flutes have no fillets, all that remains is to draw a line from each point on the fe- veral diameters from one to the other, and the lines for the flutes will be thus determined. And obferve, in all the orders a flute muft be in the center of a column or pilafi;er, not a fillet. The triglyphs are thirty minutes in breadth, fee Plate XII. and fixty-two in hei<^ht, including the conic drops, and the upper and lower fillets, with the fmall fquare above the drops. The channels of the triglyphs form a fquare or ricrht ano-le, and their breadth is determined by dividing the whole triglyph into twelve equal parts, and affigning two of thefe parts for the channels, tv/o tor the fpaces between them, and one for the half channel on each fide. The conic drops at bottom are alfo equal to two of thofe parts ; and if two parts be divided f^r !W' i\ ■4, K 4U^' u it .1, A» J6 et t^yn^/eUf^ irfttfrr'i.- j» la S9 4^_ Jf If' JiiH^itdarcluAet do-titt iy TSirraOn Jan^tXl/ft Ji/^ritSt. ( ^'I ) divided itito three, one of thefe parts will be the breadth of the upper end of tbiofe drops. The metope, or fpace between each triglyph, is forty-five minutes, or equal to the height of the triglyph without the fillets. Thefe metopes are fometimes adorned with ox fcuUs or pateras, whofe projeftions ought not to be more than the triglyph itfelf. The breadth of the mutules, without their caps, is equal to the triglyphs without their fillets. The proje£lion of the mutule is the fame ; and the foffits, or underfides of the mutules, are fometimes ornamented with drops of the fame kind as thofe of the triglyphs. The foffits of the corona are alfo enriched with rofes in fquare, and in lo- zenge* compartments, cut out of the folid, including in their depth the whole relief of the ornaments. With refpe£l to the heights and projeflions of each member, thefe muft be learned from the upright and horizontal fcales, and therefore it will be unnecef- fary to fay more. Of the Chara&er and general Proportions of the Ionic Order. See Plate X. The Ionic is more (lender and graceful than the Doric. Its ornaments, in my opinion, are truly elegant, being in a flyle of compofition between the richnefsof the Corhithian and the plainnefs of the Tufcan order: for which * In the figure of a rhomb. See Plate II. fig. 3. reafon. ( 112 ) rcafon, in the figurative ftyle, it has been compared to a fedate matron, in decent rather than rich attire. This order, being of a grave cafl-, is often employed in courts of juftice, and in the infiJe of churches, and other places of that kind : in libraries and colleges alfo, and in all places that belong to arts and letters. The general proportions are as follow : The height of the entire order is divided into five equal parts. One part is o-iven for the pedeftal, and the remaining four are divided into fix ; one of which is afligned for the height of the entablature, and the remaining five will be the height of the column, including the bafe and capital. The height aflitrned for the column is then divided into nine, one of which is for the in- ferior diameter or module. The cornice is forty-four minutes high, and its projection is equal to its height. The drip in the under fide of the corona is chamieled out one minute deep within two of the front, and oiie minute before the cyma-reverfa. The (haft of the column is fometimes fluted and fometimes plain. Twenty or twenty-four is the number of tlutes allowed, and their fillets are one third of the width. The depth of the flutes is determined by a femicircle whofe di- ameter is equal to the width of them. How to defcrlbe the Ionic Volute. See Plate XIII. Fig. 4. Operation. — Draw the perpendicular A /, and make A s equal to fifteen mi- nutes. On the center s defcr.be a circle whole diameter fiiail be equal to three and an half minutes. D.aw next a geometrical fquare, having its fides equal J ."//./'/. 2. Tl^i;- /.i TttA^ra/rn ticUn Pul^^hed Of c/ieAct directr hy (r.Terry^^^^eh^ S- 3^^'2 ^.Bar^t^Jculf* . ( 113 ) equal to the radius of the circle, as 1, 2, 3, 4. From the angles 2, 3, draw a right line to the center of the circle, as at s. Divide the fide of the fquare 1.4 into fix equal parts, as at 5, 9, 12, 8. From 5 draw the line 5.6 parallel to 1.2; draw 6.7 parallel to 2.3, and 7.8 parallel to 3.4. In the same man- ner draw 9, 10, 11, 12, and twelve centers will be found, as at 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; by which every arch of the volute will be accurately drawn, and each of them coincide with the other — thus: on the center 1 fix one foot of the compalfes, and extend the other to A: with this opening de- fcribe the arch A B. On the center 2, with the compalfes extended to B, de- fcribe the arch B C. On the center 3, with the compalfes extended to C, defcribe the arch C D. On the center 4, with the compalfes extended to D, defcribe D E, and the volute will be turned once round. For the fecond time round, begin at center 5, and extend the inftrument to E, and defcribe EG. On the center 6, M'ith the compafles at G, defcribe G H. On the center 7, with the compafles at H, defcribe H I. On the center 8, with the compalfes at I, defcribe I K, and the volute will be turned twice round. The third time round begins with center 9, from which extend the com- pafles to K, and defcribe KM. On the center 10, Avith the compafs foot at M, defcribe M N. On the center 11, with the compafs foot at N, defcribe N O. And lafl;ly, on the center 12, with the compafs foot at O, defcribe O P, which will complete the volute three times round. Obferve, that the whole volute is compofed of twelve quadrants of a circle, drawn from twelve centers, and gradually contracted in by means of the dia- gonal lines in the eye, fee Fig. 3. Therefore, as there are three complete turnings in the whole convolution, each of thefe turnings is made up of four quadrants. Hoto to graduate the Lift or Fillet of the Volute. Make the breadth of the fillet at A equal to two minutes; or according to fome, one and feven eighths, or one and two thirds. Conftrudl; a triangle, P as ( IH ) as at Fig. 5, wliofe fides AP, V P, fliall be equal to the length of the ca- thetus, or upright line AP, Fig. 4. Make AV, Fig. 5, equal to half the fide of the fquare iu the eye of the volute, Fig. 4. Draw then the line L S, Fig. 5, at a diftance from A V, equal to the breadth of the fillet at A, Fig. 4. Take the length L S from Fig. 5, and place it each way from S in the eye of the volute, or as from V to S in the large eye, Fig. 3. V S is divided into three equal parts, which are fhewn by the dotted lines; and where thefe dotted lines interfe6l with the diagonal lines in the fquare, they will find twelve new centers, which will defcribe the diminution of the lifl; or fillet by the fame procefs that was ufed in drawing the exterior contour or outline of the volute above explained. For the other enrichments of tlie Ionic capital, fee the plan in Plate XII. and obferve, that over every flute in tlie fliaft is placed an ove, or egg, iu the ovolo. Of the Characier and genej^al Proportloiis of the Compojite Order. See Plate XI. This order is generally placed last of the five, becaufe it was a compofitian from them, and of the lateft invention. But, according to this reafoning, the Doric fhould be firft in order, becaufe it was the moft ancient; however there are two reafons which have induced me to place the Compofite as the fourth. Firft, becaufe it is the fourth when orders are placed upon orders in large and magnificent buildings, where it is obfervable that the more maflive and plain columns are neareft the foundation, as fiftt the Tufcan, fecond the Doric, third the Ionic, fourth the Compofite, and laft the Corinthian. Second, be- caufe it is the fourth in point of richnefs and delicacy, for as they decreafe in ftrength they increafe in richnefs of ornaments; their elevation above the ground is therefore regulated both by degrees of ftrength and richnefs of com- pofition. But to give a proper fan6tion to this little novelty in the arrange- ment l^VB :3 ^ZP ■'■ :.53; ^3^ [it^l ^ 3 ■■■'"(' *w r-flJz« ^ jA>^^^ Off/.i/ /m =5=^ / |i /(p « « <■ rf L SE i: ^^-JiS- jl M KjT JP Ja; 1^ ¥/'<n/„/^ X ^i> fl' * o a p * OJ o6 Q-//^r/„/r '' T.Sf.avf.;iM . JO *o .Jr> tf*> I I 11 l'!illifhUasliuLA-^Jir,:-f.t h- T.Sheralaii Frf-n,.ir\ . ./->;„/..„.>>. C 115 ) ment of the orders, it may be proper to quote fome great man of this opinion. Sir William Chambers* fays, " Moil authors give the laft place to the Com- pofite order, as being the laft invented, and a compound; which of courfe ought to be preceded by all the fimples. I have followed Scamozzi's method; his arrangement appearing to me the moft natural; for his orders fucceed each other according to their degrees of ftrength, and in the progreffion that muft abfolutely be obferved whenever they are employed together." The proportions of the Compofite, and its enrichments and delicacy, being nearly the fame Mith that of the Corinthian order, in the figurative ftyle it may be properly enough termed one of the virginal orders, and -was therefore ufed in fome temples of the female deities. It is, however, generally employed in triumphal arches, for as the Romans compofed this from the Grascian orders, fo they made ufe of it in thofe fitua- tions to exprefs fymbolically their conquefts over thofe nations. I have, there- fore, in conformity to this, reprefented a trophy of war in the freeze, which I think would have a good effect placed over the center of each column, with other ornaments between them fuited to the charafler of this order. The Compofite may alfo be employed in monuments of fignal events, and in fuch buildings as are intended to perpetuate the memory of the great a6i;ions of particular perfons. The general proportions of this order are as follows-. The height of the entire order is divided into five, as ufual; one of -which is appropriated for the height of the pedeftal. The remaining four is for the height of the column and entablature. Tiiefe four parts being again divided into fix, the upper one is affigned for the height of the -whole entablature, and the remaining five of thefe parts are for the height of the column, including * From whofe excellent Treatifc on Architcclure I have borrowed I'ome of the proportions which are found in my orders, as also from Mr. Richardson's. Fa the ( 116 ) the bafe and capital. The height of the column is divided into ten equal parts, one of which is for the inferior diameter. The bafe is thirty minutes, Mith- out the upper aftragal; and the capital is feventy minutes high, adorned with the acanthus leaves, and volutes drawn by the fame method as that of the Ionic. The plan of the capital being drawn in the fame manner as that of the Co- rinthian, I fliall explain the particulars of it under that order. The foftit of the corona is divided into fquare compartments, cut out of the folid, decorated with rofes, &c. whofe relief muft not projedl more than the borders which inclofe them. In rich compofitions the foffits of the modillions are alfo ornamented, but their relief is not to exceed the horizontal fnrface, otherwife it would greatly injure the effcft of the modillion, and render the appearance of the profile of the entablature lefs pleafmg. Of the Character and general Proportions of the Corinthian Order. See Plate XII. The Corinthian, or lafl order, is certainly the moft rich and graceful in its appearance of any other. To fpeak in the figurative ftyle, it has all the deli- cacy of a female youth, and has therefore been termed the virginal column or order; on which account it is employed in the apartments of young ladies: but, for its richnefs and grandeur, it obtains a place in the palaces of kings, and the moft fuperb buildings. It is alfo ufed in public fquares, and all places of gaiety. The general proportion of this order are as follows: The whole height of the entire order is, as in all the others, divided into five, and one is given for the pedeftal. The remaining four are then divided into fix, and one part is affigned to the whole height of the entablature. The four parts which are left include the height of the column, with its bafe and .V."/J. />'. /. !"/«/<■ /3. r.-ff/jf-J ,<^//f .If* Jitvi^j- MjrfA 1^ r^:>l /\ ^''■■'-'-K ( 117 ) and capital, and are divided into ten equal parts, one of which is given for the inferior diameter of the fliaft. The bafe is thirty minutes high without the upper aftragal, and the capital is feventy minutes clear of the necking. The cornice is forty-eight minutes in height, and its projedion the fame. The foffit of the corona is worked in fquare compartments, as in the Com- pofite; but the under fides of the modillions are ornamented with an olive leaf, the fame as in the capital. The abacus of the capital is fometimcs fluted, and fometimes plain. The volutes fometimes rife higher than the under tide of the abacus, but the capital looks belt when they are bounded by the under furface of the abacus. The plan of the capital, and the pofition of the leaves as they appear on the round furface of the capital, are thus determined — Let dll, in Fig. E. be equal to the inferior diameter of the column: defcribe the arch H, g, zv, m, at pleafure; then bifeft the arch at «, and draw do, the angular line of the capital. From the angular line place five minutes each way, as at m n and n u\ Take m a and place it from <? to B; then take the whole fpace w B in the compaiit-'s, and defcribe an arch each way interfering at P. From the center P defcribe the front of the abacus m t, and fo of all the other fides of the capital. Take half the fuperior diameter of the fiiaft, and Avith it defcribe the qua- drant ere; then extend the compaffes feven minutes further, and defcribe the arch 7, which determines the projection of the firft row of leaves. Laftly, extend the compalTes to fix minutes further, and defcribe the arch 6, ^hich will determine the fecond row of leaves. Divide the quadrant ere into four equal parts, aud draw the radii dc, d r, d e, which lines will determine the fl;em of each leaf From the centers ee, draw femicircles, as they appear in the plan. From ere let fall perpendiculars, and the points 1, 2, 3, 4, will determine the fituation of the leaves in the capital. Therefore take the diftances 1,.2,, 3, 4, ( 118 ) 3, 4, from tlie plan E, and place them on the capital, as 1, 2, 3, A, each way from the center; and from thefe raife perpendiculars, M'hich will be the apparent place of the ftem of each leaf How the lea\es are formed muft be evident by infpection, and therefore I fhall not enlarge further on the fubjecl How to draw the Scotia Mouldius:. Fig. C is the fcotia, whofe height, without its fillets, muft be divided into feven. On the fourth divifion draw a line 7' d parallel with the fillets. Take the upper three parts in the compafles and draw a circle. Make de e(jual dn, or four parts. From a, draw arp indefinitely, cutting the aforelaid circle at J). Laftly, fix the compafs foot at o, and extending the other to p, defcribe the arch/>«, and the fcotia will be compleated. The cyma-re6la A is drawn from the fummits of equilateral triangles thus: draw vw, and bifedl it at x. Extend the compaffes .z' tor, and turn two arches at 3, and their interfeftion is the center for the convex part. In the fame manner y is the center for the concave part, which completes the moulding. How the cvma-inverfa B is drawn, muft; be evident by infpeftion; and with rcfpcft to any other kind of moulding, they are either confidered as quadrants, or as femicircles, or nearly fo; as the aflragals, torus, ovolo, conge, and cavetto. Obfervations on the Agreeinent of the Five Orders to each other. The height of every entire order is divided into five equal parts; of which one is given for the height of the pedeftal, and the remaining four are for the column and entablature. In ( 119 ) In the Tufcan and Doric orders thefe four parts are divided into five, the uppermoft part of which is for the height of the entablature: and the remaining four in the Tufcan are divided into feven, and one is given for the diameter; and in the Doric into eight, and one is afligned for the inferior diameter. In the Ionic, Compofite, and the Corinthian orders, the four remaining parts from the height of the pedeftal are divided into fix, the uppermoft of which is for the height of the entablature of each order ; and the remaining five, in the Ionic, are divided into nine, and one is for the inferior diameter; but in the Compofite and Corinthian thefe five parts are divided into ten, and one is afligned for the lower diameter of each column. '»' In every order the plinth of the pedeftal and its cornice are equal in projeftion; that is, .one perpendicular line ferves to determine the proje6lion of both. In every order, without exception, the bafe of each column is thirty mi- nutes, or half a diameter, high; and, in the Tufcan, Doric, and Ionic, the height of the capitals is the fame; but in the Compofite and Corinthian their capitals are each of them feventy minutes. In every order the projeftion of the bafe at the bottom of the fliaft is ten Tninutes; or, which is the fame thing, the diameter of each lliaft being divided into fix, one of them is fet forward for the projedion of the bafe. In every order its quantity of dimunition may be the fame, which is ten minutes; but in my examples the Tufcan and Doric are rather more. Laftly, all the orders, except the Doric, have their cornices to project as much as they rife; but in the Doric the cornice projects one quarter part more than it rifes. Thefe ( 120 ) Tlicfe remarks, if retained in the memory, may help to facilitate the trouble which neceflarily attends in drawing the five orders. Befides, it is fomctimes required of a workman to give fome anfwer to his employer re- fpetting the general proportions of the orders; and, if he is not acquainted Avith as much of them as I have briefly laid down in the above obfcr\'ations, he mull; of courfe look very foolifli in tlie eye of his querift, for he cannot then have recourfe to his book. But further, a workman who has profeffedly gone through the five orders, by drawing them under the direction of fome mafter, cuts but a poor figure in a converfation on the fubjeft of architefture and proportion, when perhaps, after all, he is unable to rccolle6l one fingle particular refpecting them. Of the general Proportions of Front ifpieces adapted to the Five Orders. The Tufcan frontifpiece allows fix diameters from center to center of each column or pilaftcr, as defcribed in Plate \. and page 82. The Doric allows fix and a quarter, or one third. The Ionic fix and a half; fome make it fcven and a quarter. The Compofite feven; fome allow feven and a quarter. And the Corinthian feven diameters and thirty-five minutes; or, as fome have it, eight diameters. Thefe different intercolumniations arc nearly proportioned to the ftrength or delicacy of each order, fo that the aperture, or opening for the door of each frontifpiece, is much the fame in all the orders. For though the Tufcan order only allows fix diameters, yet fix of thefe are equal to fix and an half diameters of the Doric column. And the Corinthian, though it allows at leaft feven diameters for its intercolumniation, the opening for the door-way will not, at that rate, be quite equal to fix diameters of the Tufcan column. The ( 12^ ) This fufficiently accounts for the different number of diameters affigned by architeds for the door-ways or intercolumns of the frontifpieces adapted to each order. The proportion of doors is generally in height twice their breadth ; but, in fome cafes, a little more height is requifite. The width of the door is divided into four equal parts ; one of which is for the diameter of the column, or breadth of the pilafter. Half a diameter is added to each fide of the column, for the impofl or ground which receives the proje£lions of the plinth and capital. Half a diameter is alfo allowed above the door to the underfide of the archi- trave, and one for the fub-plinth, or the fquare part on which the bafe refls. According to this proportion, from the top of the fub-plinth to the top of the column there will be feven diameters and an half j which will be within half a diameter of the full fize of the Doric column, according to the order ; but if there be a ftep up to the entrance of the door, this will incrcafe the column to its full height, which is eight diameters. To the height of the column mufl be added two diameters for the whole entablature above the capital : and for every other particular refpeding the mouldings, the reader muft have recourfe to the orders themfelves. General DireBions for drawing the Five Orders in Indian Ink, It is befl to procure wove paper, becaufe its fubflance will bear a better fhade, and its quality gives a more handfome appearance to a drawing, than the more common fort. The paper fhould be regularly damped, and pafted round the edges, fo that when it dries it will become tight and even in its furface. Q;--Z Proceed ( 172 ) Proceed then to draw a perpendicular line for the axis of the column, and on this line place the feveral heights required. Through each of thefe heights draw, by the pencil, lines at pleafure parallel to the bafe. Next find the inferior diameter of the column, and afterwards the fuperior one. From the extremities of the fuperior diameter draw perpendicular lines upwards, and from the extreme points of the inferior diameter draw perpen- dicular lines downwards to the top of the pedeftal. From thefe lines place the projedion of the bafe, and from the projedion of the bafe each way, draw two other perpendicular lines down to the bafe of the plinth. Thus far the drawing is prepared for laying on the proje£lions of the feveral members which take their fpring from the above perpendicular lines, and when the mouldings are all drawn by the pencil, the flrokes of the pencil ihould be tendered or made fainter by the Indian rubber, fo that the ftrokes of ink may be more clearly feen as they are drawn, and prevented from being too ftrong, which if they are, the drawing is totally fpoiled. If the drawing be on a large fcale, as thofe on the right in the plates, the compafles may be fuccefsfully applied in drawing the curved members ; but if they are fmall, like the finiflied and entire orders in thofe plates, they muft be drawn by a fine pointed camel's hair pencil, guided by a ftcady hand. The application of any kind of writing ink to the outlines of the drawing muft always be avoided, becaufe it neither agrees with the nature or colour of Indian ink. The writing ink not only makes an outline too harfh in appear- ance, but likewife deftroys the effeft of the Indian ink ; becaufe the water that is mixed with the Indian extrads the quality of the writing ink, and of courfe they blend together in one mafs, and the fhadow becomes partly blue and partly black, which deftroys the harmony of the whole. Therefore mix good Indian ink by rubbing it on a marble ftone, and let the ink fland a few hours, till the grofler particles fettle to the bottom. Add a little water to a part of it, to make a light fhade with ; and with this light kind mark the outlines of the column, applying the hair pencil to the curved parts, and the brafs pen to thofe which are Itraight. After After this procefs rub the drawing quite clean ; and obferve this as a ge- neral maxim, that the fainter the outhne the better, provided it can juft be difcerned. The next things to be confidered are Ught and fhadow, which are oppofite in themfelves ; but if difconne£led, no good efFe£t can be produced in a draw- ing. Wherefore, where a flrong Ught is fuppofed, there mull: alfo be a ftrong Ihadow agreeing with it ; and where the hght is weak, the fliadow is lefs dark in proportion to it. Rays of hght do not project (hadows contrary ways at the fame time. Therefore the poiiit of hght muft be fixed in the mind at leaft, if not on the paper, from whence the rays are diredled in parallel lines to the objedl, which produce a fhadow on the contrary fide to that which the light comes from. Proceed then to lay on a weak tint on that fide of the fhaft which is oppofite the light ; and the breadth of this tint muft be proportioned according as the light is fuppofed to come, either diredly on the front of the pidlure, or ob- liquely to it. If the hght comes on the front, the tint is narrow ; but if ob- liquely on the pidlure, the tint is broader, or comes farther on to the center of the fhaft, in proportion to the degree of obliquity. After having laid on the firft tint according to thefe principles, a fecond tint muft be applied in darker Indian ink ; but the dark tint mufl not be carried full to the outline of the dark fide, becaufe that would deflroy roundnefs ; for, in nature, all round or cyhndrical bodies have a refleded light ; but this refledled light is not equal in ftrength to the direft hght, wherefore the firfl or weak tint of Indian ink is fuppofed to be equal in degree to the refleded light, confequently a fmall por- tion of the firfl tint is left on the edge of the fhaft, which is graduated or foftened into the fecond tint, which is flrong, producing a mafs of fhade, blending; itfelf in reofukr gradation with the firft tint towards the center of the fliaft. After the fecond tint is perfectly dry, a third ftill flronger fliould be applied, in order to complete a high-finiflieJ drawing; but care muft be taken to lay it on about the center of the fecond tint, and not broad, but folid, fof- tened a little off at the edges, which will produce a fufhcient roundnefs, if rightly managed. Q^Z z If ( 174 ) If the (haft is reprefented as fluted, its fhading will yet require more ma- nagement; but the fame principles muft be obferved. In managing the flutes, it will be proper to mark their boundaries firfi: with a nice brafs drawing-pen, filled with thin Indian ink, that it may diftribute and pafs eafily through the pen, leaving a very faint line on the light fide, fcarcely to be feen ; but in rulinsf the dark fide the ink mufl: be laid on fl:rons;er, that the outline of the flutes may not be totally loft when the fhade is laid on. After the firft tint of (hade is applied, it will be requifite then to touch in the dark fides of the flutes. Thofe on the dark fide of the fhaft may be done by the hair pencil ; but if the drawing is on a fmall fcale, the brafs pen will do much better on the light fide; becaufe, by drawing parallel lines with that inftrument in imitation of graving ftrokes, it will produce a fhade in the flute more confonant, and in better tone with the light fide of the fhaft, than can be performed by the hair pencil. The flutes on the dark fide of the fhaft muft not be all black, for their con- cavity will refleft a dim light oppofite to their dark fide, upon the fame prin- ciples by which light is refledled on convex furfaces. Laflly, when the flut- ings are thus handled, a fecond tint of Indian ink muft be laid on at the dark fide, by which the flutes and fillets muft be made to harmonize, and appear in one mafs of fhade, without deftroying their diftindlion. In general, the fecond tint is ftrong enough for fluted fhafts, becaufe the outlines for the flutes con- tribute towards a fhade themfelves. The mouldings muft next be confidered ; and as thefe are in a different po- fition from the fhaft, confequently the light muft ftrike them differently. In the examples given, I have fuppofed the aperture, or point of light, above the top of the column ; which is a fituation highly advantageous to the drawing, becaufe, upon this principle, there will be a regular ftrong fhadow under each covering member produdive of a good effedl. Hence, in the Ionic, for inftance, the hollow, or upper part of the cyma- redla, has a ftrong fhade ; and the fwelling part is light in the center, bearing a fhade downwards as it recedes back. The corona is alfo light, becaufe the rays come full upon it ; but the cyma-reverfa, dentils, and ovolo, are all in 3 fhadov/. ( ^IS ) fhadow, on account of the large projeftion of the corona, which fcreens them from the light. The left hand volute projefts a (hadovv on the (haft, and the curved top of each flute does the fame. The lower ends of the flutes are lio-ht, for the rays come full upon them ; but the upper part of the fcotia in the bafe bears a flrong (hade, becaufe it is totally covered by the projedion of the upper aftragal. The cornice of the pedeftal is nearly all in (hadow ; but the bafe is nearly all light, for there is nothing to prevent the rajs falling upon almoft ^wtxy part of it. Thefe obfervations, with the exercife of a little tafte and eood lenfe. wiH, I prefume, enable the learner to accompli(h his attempt to fliade the five orders in fuch a manner as will do him credit. END OF THE FIRST PART. PART THE CABINET-MAKER AND UPHOLSTERER'S DRAWING-BOOK. IN FOUR PARTS. Part I. Containing Ufeful Geometrical Lines, on Seven Copperplates, applied particularly to the Cabinet and UphoUtery Branches. Alfo the Five Orders of Architedurc, on S x Plates; with feme Account of their Antiquity and Charaitter; together with the Names of the feveral Mouldings, traced from their Origin. Being the Second Edition, with Improvements. Part II. The Elements of Linear Perfpeftive applied to the Art of reprei'enting various Kinds of Furniture ; with Pradical Remarks on Shadows projedled by the Sun, confidered in different Situations to the Pidture; the Whole illultrated Od Copperplates Part III. A great Variety of Original Defigns, in Beds, Chairs, and every other Article of Houfehold Furniture in the neweft and moll approved Style. Among which is a mod fuperb Englilh State-Bed, with Ornaments emblematic of the Britifh Government explained in Letter-prels; together with a Seftion and View of the Prince of Wales's Chinefe Drawing-Room, and other Articles of Importance which cannot here be inferted. Part IV. Ornaments adapted to the Cabinet and Chair Branches ; including a Variety of Chair Legs, Elbows, and Splads, Borders, Centers, Tablets, and Legs for Pier Tables; alfo Bed Pillars, Window and Bed Cornices ; Pediments, Tripod^ Candle, and Flower-Pot Stands ; Girandoles, Glafs Frames, Pilafters for Commodes and Book-cafes, Cornices at large, their Spring ftiewn, and the Manner of contradling or enlarging them from any given Pattern. THE WHOLE CONTAINING ONE HUNDRED AND TWENTY ELEGANT ENGRAVINGS. By THOMAS SHERATON, Cabinet-maker. Recommended by many Workmen of the firfl: Abilities in London, who have thcmfelves infpefted the Work. PART LONDON: PRINTED, BY APPOINTMENT OF THE AUTHOR, FOR G. TERRV, N° 54, PATERNOSTER-ROW. 1794- N. B. The Author bogs leave to obfcrve, thnt notwithrtanding this Drawing-Book is principally dcfigned for Cjbinet-malcers and Upholfterers, yet he is pcrfiiaded that it will be found of great ufe rr. many other branches that are any way concerned with drawing ; accordiirjily he can affure the Public, that perfons of various other profeffions have already become Subfcribers, as Chair-makers, J.)iiiers, Smiths, Carvers, &c. [ tintcrcD at stationers (^all. ] THE CABINET-MAKER, AND UPHOLSTERER'S D R A W I N G - B O O K. PART 11. ON PRACTICAL PERSPECTIVE APPLIED TO THE ART OF REPRE- SENTING ALL KINDS OF FURNITURE IN DIFFERENT SITU- ATIONS t COMPREHENDING A REGULAR AND FAMILIAR TREATISE ON THIS USEFUL SCIENCE, DIGESTED AGREEABLY TO THE author's OWN EXPERIENCE IN THE ART FROM SOME YEARS PRACTICE, AND FROM OBSERVATIONS ON THE PRINCIPAL WRITERS ON THE SUBJECT; VIZ. DR. BROOK TAYLOR, DR. PRIESTLEY, MALTON, KIRBY, NOBLE, AND SOME OTHERS. INTRODUCTION. That the knowledge of perfpedtive is highly ufeful to Cabinet- malcers, Upholfterers, Chair-makers, Joiners, and other per- fons concerned with deiigning, cannot be difputed on good grounds. And, though this is an indubitable pofition, yet many in the above profeffions are not fufficiently, if at all, ac- quainted with it. This defedt, in their education or neglect in their own apphcation, neceffarily fubjeds fuch to conliderable .Z di fad vantages, ( 178 ) difad vantages, both with refpecSl to giving and receiving orders- A matter cannot pollibly convey to the workmen fo juft an idea of a piece of furniture by a verbal defcription, as may be done by a good fketch, proportioned according to the laws of per- fpe(5live, and fituated fo as to give the moft general and clear view of the whole piece. Nor, on. the other hand, can a work- man fo well underftand the meaning of a drawing, and what it is intended to reprefent, witluout fome knowledge of tlie art I am pleading for ; and confequently his progrefs in executing the work will be proportibnably retarded, and, perhaps, not fo exaiftly finiflied at lalt. On thefe accounts it is a mafter's iii- t-ereft to know perfpective himfelf, and to have men about him that underftand it. When this is the cafe, time is often gained, ftufF fpared, and difgrace avoided; fince it is matter of fact, that many alterations in pieces of work of every kind take place; fometimes owing to bad fketches or drawings,, and fometimes from want of underftanding a good defign when it is given to work by. There are. fome mall^ers, indeed, v.- ho will fcarcely allow their foremen time to make any kind of fketch ; but, if I may offer my opinion on this head; I mull fay that fuch a me- thod of carrying on bufinefs neither refledts honour on the foreman, nor in the end turns out to any advantage to the mafter; but, on the contrary, frequently a conHderable lofs.. Belldes, ( 179 r Befides, as it is the prefeiit mode to introduce much paint- ing in furniture, it is of great ufe to know perfpedlive, in order to underftand when fuch painting has its proper effedt, and to enable the director of work, whether mafter or foreman, to point out fuch improprieties as may efcape the notice of the painter ; and which, if entirely overlooked, might prove injurious to the work, and ofFenfive to a cuftomer of tafte. To thefe we may mention another advantage that oftert arifes to a mafter from knowing this art; fince, by it, he may often fix the judgment and mind of a gentleman or lady re- fped:ing the piece of furniture they wifh for, by producing either a drawing that has been previoufly made, or by being able, off hand, to furnifli their ideas with a good pencil fketch. In fliort, a good perfpedlive drawing may be fent to a gentle- man or lady in the country, with almoft as much confidence of fuccefs as if a model of the piece of work were fent. Laftly, if the reader confider himfelf a gentleman, or as pofTeflTed of a liberal education, and at the fame time entirely unacquainted M'ith this fine art, it will carry in it an air of con- tradi(5tion ; becaufe perfpe(ftive is founded on geometrical and optical reafoning, and has therefote always been confidered as a branch of the mathematics and of a liberal education. Yet it is my intention not to treat the fubjed mathematically, , Z 2 becaufe ( i8o ) becaufe many have done it already in fiich a manner as far ex- ceeds any thing I can pretend to; and becaufe it would not fiiit workmen, for whom the following treatife is intended. If, however, any other above this fphere can reap any information from it on account of its fimplicity, I lliall be happy to have ferved them ; but if he be above receiving inilrui5lion through that channel or medium which is only intended to convey the knowledge of this art to workmen, the reader may confult fome of thofe authors referred to in the title, where he will fee problems, theorems, demonftrations, and corollaries enough to fill his leifure hours w ith, and to carry the fcience to any length he pleafes. However, to look into fome of thefe books would greatly difcourage many workmen, and even fome others of a higher clafs, who diflike the drudgery of perufing and com- paring an infinite number of references to a variety of fcliemes, which are rather more calculated to fliew how far the fubjeifl may be carried by mathematical fkill, than to inform the reader of fuch principles as may be wanted in the practice of the art, or to give him a tolerable view of the theory on which the fcience is founded. And it may be afligned as one reafon why the fabjetft of perfpedtive is fo little known amongft workmen, that it has been treated too mathematically. For, though geometry muft afiift in Hating theories, and in making new and additional dif- X coverios ( i8i ) coveries of the principles of the art, yet we mull: not infer from hence that a workman cannot learn the pradtice of the art with- out being acquainted with that fcience. Malton fays the fame thing in the preface to his Treatife on- Perfpedtive. " Perhaps," he obferves, " the demonftrations of the laft (meanmg the lafl theorem of his fourth fedtion) may deter thofe who are not geometricians from examining it with that attention it requires ; let fuch remember, that, in order to pradlife perfpedtive, it is not abfolutely necelTary to be a geo- metrician, becaufe I pracStifed it long before 1 underftood geo- metry." hi fine, I fliall only fay, that it has been my aim to put into the hand of the ingenious workman fuch a view of the fubjedt of perfpedtive, applied to a general variety of cafes, as may enable him to get through with defigning any thing he meets with in the courfe of his bufmefs : and if any thing more than this be found in this treatife, the reader will fee more than what is promifed ; which may probably incline him to ac- quiefce with the author's fentiment, that it is better to do more than we fay, than fall Ihort of what we have promifed. ''^ section: ( iBa ) SECTION I. Of the Principles on "dohich Perfpeciive is founded^ and the Defini- tions of thofe Terms neceffarily ufed on the fubje&, • The principles on which the art is built are founded on the nature of our fight, -which invariably comprehends all objects under fome angle of a lefs or greater degree, in proportion as the obje<5t is at a greater or lefs diftance from the eye of the fpedtator. Hence let A. Fig. i. Plate XIV. be confidered the human eye, which is nearly globular; and P the pupil*, or that ex- tremely fmall point of the eye into which the rays of light if- fuing from every part of illumined objects in right-lined direc- tions all conver^ge. * The term pupil, in general, means a youth or minor under the tuition and manage- ment of a mafter or guardian ; but why it has been introduced into optics, and apphed to the aperture or fmall opening of the eye which receives the light, is owing to the little image — or pupUla, a puppet — which is reflefted in the eye, and feen by every one who looks fteadily on it, which is no other than the fpeftator himfelf, whofe image in miniature is reflefted on the cryftalline humour. Thus 1} B 7\Shfi,; rtlp. .\".'/.r. ///. /. J^/f//it/f/a/v Jy*r//r.\'. .)' i /^ArA.jr; ^ '^ 5 IT f - ^^^ \\ \''' w""""^ ^^^-^^ Tl yAly 2. \J ^^^^ __^^ ~\ /A-^ 1 ^"^~->^ ( TShfia^,-r, />^/ JPn/'/i/fu-.f as t/it A^t i^itvrfs In' '' Trrrf.- May 2^*J/rpi f/far-&n*' .V,a^ ( i83 ) Thus the rays BP and DP, iflliing from the ferpentine figure B D, are faid to converge, becaufe they unite in a point at P, the pupil; and, after palling through the pupil and con- tinuing in- their dire6l courie, they diverge or fpread open as at nmrqv.t^ on that part of the eye called the retina*, by which an object is formed fimilar to the originals B D, EC, FG, and in magnitude according to their different diftances from, the eye t.. Therefore, as the firft object BD is neareft to the pupil P, the points;/^ on the retina are moft extended, becaufe the angle DPB, under which the object BD is feen, is conliderably larger than thofe under which the objeds EC and FG are feen.. And again, as the fame object is removed back to- EC, the rays are lefs extended on the retina as at m v ; but if the obje(5l be removed ftill further from the fight P to F G, the rays will, ftill diverge lefs, and confequently the objedl painted on the re- tina will' be proportionably fmaller as at 7~q> And thus, by re- moving the obje<Sl F C ftill further and further from-, the fight,, it would be feen. ujicler a proportionably fmaller angle, until. * Retina, from rcte, a net ; becaafc this part of the eye Is a fine expanded membrane, fomewhat open like a net, and fpread over the bottom of the eye, on which are painted the pidlures of all the objc6Vswc perceive. t The refradlion of the rays of light occafior.ed by their pafTmg through the dirfcrent' mediums or humours of the eye, has nothing to do with perfpedlive ; it belongs to optics only, on which Fergufou's Le<Slurcs m.iy be confulted, and others on the fubjeiSV. it f i84 ), it would at length vanifli into a point, and lofc its appear- ance. That the rays of hght, by which we are made fenfible of ohje6\s, make their way to the organs of fight in right-Uned di- rections, is evident from a mofl fimple experiment: for, if the bore of a tube or pipe be as much curved as is equal to the di- ameter of the bore, nothing can be feen through it ; or if one objck!!: ftanding before another of equal magnitude on the fame line, be viewed by a perfon ftanding on that line, the laft will be hid, provided they both ftand upright. I fimply mean, if the fliafts of two columns of equal diameters were placed up- right and a fpectator were ftanding upright on a line paffing through the centers of each fliaft, the laft one could not be feen; but if vifion, or the faculty of feeing, were performed by rays of light in curved dirciflions, perhaps this would alter the cafe, but not for the better, as I am certain that the conftrudtion of our eye, and the way in which we, at prefent, difcover objeds, are the perfedt produdions of Infinite Wifdoin- From what has been faid and referred to in the figure, I prefume that the reader is not altogether ignorant of thefe two things ; firft, that all objedls api>ear to the fpe(5tator proportion- ably lefs the further they are removed from the eye; and, iecond, that the rays of light coming from every part of il- lumined ( iSs ) liimined obje6ls operate on the eye in right-lined direaions. Thefe two propofitions being admitted as certain truths, two very conliderable points in perfpecSlive will hereby be gained. Firft, that in the reprefentations of obje<5ts originally of the fame dimenfions, thofe which are furtheft from the front of the pidlure mud be leaft, in proportion to the fuppofed or real dif- tance of the fpedator's eye from the obje6t : and fecond, that ' a right line from the top and bottom of the front objedts, ter- minating in a point on the horizon, will determine the heights of all thofe back objeils which are originally of an equal height with thofe on the front. Hence, if a range of columns be reprefented on a pidure, a right-line from the top and bottom of the firft column to fome point in the pidlure, will determine the heights of all thofe be- hind. Experience will convince us of the truth of this : for if we place ourfelves at a diftance from a ftraight row of columns flanding a little to one fide, and looking attentively from the firft to the laft column, we fliall then fee that the pillars will appear to diminifti backward in the form of a triano-le; or in other words, the tops and bottoms of each column will feem to tend to one point. The fame may be obferved by ftanding clofe to a long brick * * I particulaiife a brick wall merely on account of the joints being much clofer to each other than thofe of flone; which circumftance makes the perfpedive diminution more apparent to a learntr than in thr joints of ftone walls. A a wall. ( 186 ) wall, and ranging the eye along the joints of the bricks ; we fliall fee each joint feemingly terminating into one point. Thofe joints below the eye will appear to rife up, and thofe above it will feem to lower; and if the length of the wall were continued as far as we could fee, the joints would apparently unite in one point. Thefe fimplc experiments cannot be accounted for upon any other principle than that which I have already advanced on the nature of vifion ; namely, that all objefts, as they recede from the eye, are feen under a fmaller angle in proportion to the diftance of the object from the eye. This propofition holds good, not only as it relates to the heights of objeds, but alfo to their breadth and thicknefs, for thefe are diminiflied or con- tradied by the fame rules, founded on the nature of our fight. Nor are thefe remarks to be reltridled to fuch obje<5ts as ffcand upright on the ground, for thofe which are horizontal in their pofition, or which are lying in various fituations on the ground, are all fubjed to the fame laws of diminution. But it muft here be obferved, that the various pofitions of objects give birth to moft of thofe imaginary planes which are introduced into the fvibjeit of perfpeilive ; for in thefe planes all the variety of obje<5ls that we can conceive of, are fuppofed to be lituated fome in the ground-plane, and others parallel to it, both above and below the horizon ; fome in upright, and fome in oblique or inclining planes. And this variety of planes Iliould be under- ftood ( 187 ) flood and carefully diflinguiflied by the learner, before he can make any good progrefs in the art, or know what he is about, when he begins to reprefent. Thefe planes are again bounded by fo many right lines, of which they are compofed ; and thefe lines have their names anfwering to their intended ufe in the practice of perfpec- tive. Since, therefore, planes, lines, and points, comprehend the whole art of perfpe(5tive, it will be requifite to define thefe in as clear a manner as poffible. The reader will, perhaps, ima- gine here, that I am drawing him into the lludy of geometry, as an clTential requifite to the pracStice of perfpedtive, and there- by contradi6ling what I have already advanced in the preface. If, indeed, to exercife our reafoning faculties, and to make ufe of a little common fenfe, be termed the ftudy or knowledge of geometry, I will aver that no man will ever learn perfpe<5live without thefe. But this every one knows ; that many can ex- ercife both good fenfe and reafon who never faw nor heard of Euclid. Befides, if the reader has attended to the firft part of this work, in which lines, fuperficies, and folids, have been touched on in a general way, he cannot be confidered as totally ignorant A a 2 of ( i88 ) of fome part of geometry which is ufeful to the knowledge of perfpedlive; however, as I have faid nothing of planes and their interfedtions, I fliall here explain them, fo far as they re- late to the fubjeil of perfpedlive. Of the Nature of Planes relative to the Subjecl of Perfpe&ive. A plane, ftritSlly fpeaking, is an even furface, neither con- _ cave nor convex, but which will agree with a ftraight ruler or line every where. A plane, in theory, may be confidered indefinitely, or de- finitely. When it is fuppofed to be indefinite, it admits of no bounding lines, but is imagined to be continued without limits. When it is defined, its boundaries are limited by lines, as AB, BO, OD, and DA. Fig. 2. In perfpe(5live there are five planes principally in ufe, ac- cording to Dr. Brook Taylor's fyflem; but the various circum- ftances of obje(Sts in the pi<5lure frequently produce a variety of others, which, however, are not termed the elementary planes, as the above five may, but only accidental, depending on the circumftances of objects. 0/ u 189 ) . .'ii: Of ths Ground Plane. In the order of thefe planes I fliall confider the ground plane firft, being commonly a horizontal furface on which ori- ginal objects have, in general, their feats or foundations; as 1, 2, 3, 8, is the feat of the cafe of drawers on the ground plane A B, DO, Fig. 2. The Do6tor terms the ground plane the original plane, *' By which," he fays, " we mean the plane wherein is fituated any original point, line, or plain figure." I fliall, in general, however, ufe the term ground plane, as being more fimple, ex- cept in cafes where no regard is paid to its being horizontal % then, indeed, the term original plane muil be ufed, being more comprehenflve, as it includes any pofition. Of the Perfpediive Plane, Second, the perfpe(Slive plane, otherwife called the plaue of the pidture ; which, in general, is a plane perpendicular ta that of the ground, as GR, H L. This plane is to perfpecStive what the retina is to optics; for the images of all original objects are delineated on. both. The ( I90 ) The perfpeiSlive plane may be confidered as fome tranfparent medium placed upright between the objedt we view and our eye ; and as the rays of light coming from every point of illu- mined objects converge, in right-lined diredlions, to a point on the pupil P, Fig. 2, a feftion of thofe rays, produced by this tranfparent medium or perfpecftive plane, is the perfpedtive re- prelbntation of the original obje(ft, be it what it may. Hence, let the learner place himfelf before a glafs window, which is, proi)erly fpeaking, the perfped;ive plane to every ob- jetSt he looks at through it ; and as thofe objedls appear to him on the window, fuch is their perfpeftive reprefentations on the paper, board, or canvafs, we draw on. The appeaiance of ob- ie6ls on a window may be found by gumming the glafs, which does not deftroy its ti-anfparency, but makes it capable of receiv- ing a mark ; and if the eye be kept perfe<5lly Iteady to one point in the window, and with a pencil, the points or angles of a houfe, for inftance, be marked as they appear on the glafs ; and when this is done, if right lines be drawn to each point, thefe lines Avill form the perfpe<5tive reprefentation of the houfe. Thus the plane G R, M L, may be confidered a piece of gummed glafs fixed upright on a table or ground A B, DO; and at P is the fpe6lator's eye, viewing through the glafs the original object i, 3, 5, 7. The right lines ifTuing from every part of the objedl and converging at P, reprefent the rays of light ( 191 ) light paffiiig through the tranfparent medium to the eye P. Now, as the original objecSt is defcribed on the glafs by the di- rection of thefe rays, if the fpedtator, with his hand, mark the points I, 3 — 5, 7, 4—6, and afterwards join the points by right lines, this will be the exadl perfpedtive reprefentation of the original objedt. Simple experiments of this fort fliould be pradlifcd, as I am perfuaded they are more calculated to teach the principles of the art than long and tedious theories *. Of the Horizontal Plane, The horizontal plane, or plane of the horizon, is, in per- fpedlive, an imaginary plane palling through the eye of the * An artift lately Inforined me, that a piece of ground gbfs, unpolifhed, and ofled over with fweet oil, is the bed for this purpofe ; for the oil gives a degree of tranfparency to the glafs that admits of objects being feen through it, and its artihcial roughnefs makes it eafy to draw on. If a fquare of glafs of this fort be put in a flight frame of wood, fixed upright on a plain board, and there be a fight-hoIe made in a piece of wood fixed perpendicular to the fquarc of glafs ; and if the fight-hole be fixed from the glafs equal to the diftance P s, and to. the height of the eye P N, then every thing which relates to Fig. 2, may be proved by ocular demonfiiation, provided the learner ufe this little inft:rument according to the references made to this figure in the diflSerent heads of this feftlon. fpedlatoF, ( 192 ) ipcilator, and being perfe6lly parallel with the ground plane, it cuts the vipright pidlure or perfpedlive plane at right angles. Thus, in Fig. 2, Plate XIV. F H, L M, is the horizontal plane, whofe perpendicular height from the ground plane A B O D is the height of the eye at P ; hence P N is the perpen- dicular height of the eye, becaufe the line P N is perpendicular to both thefe planes. The horizontal plane F H, LM, being produced, it necef- farily cuts the perfpedive plane G H, L R, at right angles, and the interie<5lion of thefe two even furfaces or planes with each other being a right line as H L ; hence we have what is com- monly called the horizontal line H L ; or, more properly, the vanifliing line of a plane parallel with its original. And as the interfecflion of the horizontal w ith the perfpecftive plane pro- duces the vanifhing line H L, fo the interfedlion of the pi(Slure with the ground plane produces the bafe or ground line GR. All original obje6ls, as they appear to come into the plane of the horizon, gradually vanifli into a point, and difappear. Hence the application and ufe of the term horizon in perfpec- tive, which literally means the limits or boundaries of our fight, from " 'c^t^a>, borizo^ I limit or bound." The further ob- je£ts are reprefented from the front of the picfture, or from the ground ground line G R, the nearer is their approach to this plane, arid confequently their apparent magnitude will be proportionably lefs, as has been already demonftrated in page 183. For if the cafe of drawers, in Fig. 2. were removed conllderably further from the perfpeftive plane G R H L, it is evident that the rays I P, 3 P» 5 P» 7 P» ^c. would not fubtend * fo large an angle on the plane of the picture as they do at prefent : it is alfomanifeft that thefe rays will alfo rife higher on the pi6lure in proportion as the cafe of drawers or original obje6l is removed back, confe- quently the image i, 3, 5, 7, of the drawers on the pidlure would approach nearer to the horizontal plane, until at length the image on the pi(Slnre would totallj^ vanifli at s, the center of the i:)i<5ture and height of the eye. To underftand this yet more clearly ; fiippofe the drawers to be brought forward clofe to the pidure, then the foot i would be at 10, and the foot 3 at 12, on the interfe6tion or ground line GR, and the image of the original objedl would then appear as large on the pidture as the original itfelf ; for then the point 5 on the drawers would be at a on the pidure, and the point 7 at d ; but the whole image of the original, in this cafe, is lower on the pidlure than before, and confequently forther from the ho- rizontal plane, which was to be fliewn. * Yromfub and tendo, I ftrctch. The fubtenfeof an angle coinciJes witli the chord of the arch. Thus the objeft B D, Fig. i, fubrends an angle of 60", for the rays B P D P cut rhcarchin that proportion ; and therefore the objca BD is faid to be ktn under m-i angle 60^ R b From ( 194 ) From what has been faid, it is obvious that the whole fpace on the plane of the picture for delineating objeils, is compre- hended between the ground line GR and the horizontal or va- vifliing line H L. No objedl can with propriety have its feat on the picture below the line GR, for this line is the interfedtion of the ground plane with the plane of the pifture; and therefore, to reprefent the cafe of drawers lower than at lo and 12 on the ground line G R, ^yould lead us to fuppofe a new ground plane below the firft, and a new horizon to fuit it, other wife the draw- ing would be unnatural and diiforted. On the other hand, no original objedl can have its feat in the perfpedtive plane higher than H L, for the line H L marks out the interfeftion of the horizontal with the perfped:ive plane; and as the plane of the horizon is generally the vanifliing plane of all original objects fituated on the ground, their feats in the pi6ture cannot be above the vanifliing line H L, without prc- ducing worfe efFedls than in the other cafe juft mentioned. Fcr if the images of all original objects, however large, vanifli into a point s in the vanifliing line H L, it would be prepofterous to fee a tall obje<5t feated on this line, or above it. Before I quit this head, it will be proper to obferve, that the horizontal plane, on which I have feemingly laid fo much ftrefs, does not poflefs any thing peculiar to itfelf, owing to I its ( 195 ) its being confidered 'a plane, perfeftly level ; for all the various poiltions of vanifliing planes make no rlifFerence in theory, pro- vided they are confidered as parallels to original planes. It is the pofition that thefe planes have to each other that is to be regarded. This was one principal difcovery which Dr. Brook Taylor made in his new fyftem of perfpeftive, and which has rendered his principles fo univerfal. In his book he fays, " He makes no difference between the plane of the horizon and any other plane whatfoever ; for fince planes, as planes, are aUke in geometry, it is moft proper to confider them as fo, and to ex- plain their properties in general, leaving the artift himfelf to apply them." Yet it may be obferved, that we have a natural prejudice in favour of fomething peculiar to the horizontal va- nifliing plane; becaufe, in nature,, the laws of gravity fettle all folid bodies in a horizontal pofition : this being the cafe, we are accuftomed to view objeas in this form, and of courfe are re- quired to draw them fo ; therefore, in the praftice of perfpec- tive, the horizontal vanifliing plane is generally wanted ; but in principle and theory, the relation that one plane has to another is only to be regarded. Bb2 Of ( 10 ) Of the Directing Plane. The diiedling plane is imagined to be parallel with the pidture, whatever pofition it is fuppofed to be in ; and its diftance from the plane of the picture is equal to the diftance of the eye of the fpe6lator ; therefore it is confidered as a plane paffing through the eye, as the plane M F VU, Fig. 2. Hence if any original line Z X be produced till it cut the direfling plane MFVU, a line drawn from Y, where it interfedts, to P, the place of the eye is termed the directing line of that original lineZX. And the reprefentation of any original line in the plane of the pidture is always parallel with its diredling line in the di~ renting plane. Of the Vertical Plane^ In perfpe<5live, the vertical plane is confidered as perpendi*- cular both to the ground plane and the plane of the pidlure ; cofidfequently it cuts the other four at right angles. The plane PjQN, ( 197 ) P J QN, Fig. 2, is thus termed geometrically, becaule it is in a direilion perpendicular to the horizon ; but in perfpe6tive it may be in any poiition, provided it be perpendicular to the original' and perfpe6live planes, and at right angles with the other. The interfe(5lion of this plane with the pi(5ture HLGR pro- duces the perpendicular line j- Q, termed the vertical line of the pidlure ; and the vertical plane being continued till it cut the diredting plane in the line FN, that line PN is the interfe(Slion of the vertical with the diredting plane; and as sQ, the vertical line of the picSture, is parallel with P N the interfedlion of the; vertical with the diredling plane: PN is therefore the diredting line of s Q, the vertical line of the pidlure. Vertical planes have vertical vanifliing lines when the pic- ture is perpendicular to the ground plane ; in which- cafe the vertical line jQ is continued to a length above and below the horizon H L, that will admit the neceflary vanifhing pointSi. Of ( 198 ) Of the VifiialFlam. ■ i To thefe planes already defcribed may be added the radial, or vifual planes. A vifual or radial plane, is fuch as pafles through the eye, and any original line whatever. A plane may be continued by any three points. The three points PXY are the interfedlions of three right lines ; and, ac- cording to geometrical reafoning, when three fuch lines meet each other, >s the lines PX, X Y, and XYP, they are all in the fame plane. This, among geometricians, is an axiom or felf- evident truth, and therefore needs no demonftration. The continuation of the plane PC YX, which the triangle Y P X is in, till it interfe<£l:s with the plane of the pidlure, is therefore the vifual or radial plane of the original line ZX ; and the line v i6, produced by the interfedtion of the vifual plane with the plane of the picture, is termed the vifual line of the original Z X. . As I have already obferved and proved that the appear- ance of objeds on the retina is conveyed by rays of light flow- ing {( '199 ) ing from every point of any objedl to the eye in right-lined di- reaions, fee page 184; let the right lines XP, ZP, beconfidered as the rays of light coming from thfe original obje<5t Z X, and con- verging at P; but thefe rays are cut or interfedted by the plane of the pidure G R H L at a; s, therefore the line x z is the pro- jeaion of the original objea Z X on the plane of the piaure ; or, in other words, it is the perfpeaive reprefentation of the original objea ZX: for the reprefentation x z of the original line ZX is in the line v 16, which is the interfeaioix of the vifual plane P C Y X with the plane of the piaure : and fince the line PC is the parallel of the original line YX, where PC cuts the plane of the piaure at <z;, proves that the line v 16 is the true line of interfeaion produced by the vifual plane cutting the plane of the piaure. Hence the line -y 16 is, in perfpeaive, termed the vifual line, from vi/ro, I fee; the lines PZ, PX, are the rays of light by which vilion is performed, or by which we perceive objeas, and as the interfeaion of thofe rays is in the line v 16, fo this line v 16, drawn on the piaure, is properly termed the vifual line of its original ZX. Of ( 200 ) Of the Lines in Per/peciive generated or produced by the foregoing Planes. I HAVE already fpokeii of thefe lines in the explanation of the feveral planes to which they are related ; but it will alfo be requifite to fum them np here, that the learner may have a more clear view of them from what has been faid. Firft. — The ground line GR, is a line produced by the in- terfe(5lion of the pidure or perfpecflive plane HLGR with the original plane ABDO. It may alfo be fimply termed the in- terfecflion of the picture ; but fome choofe to call it the enter- ing line. Second. — The vanifliing line H L, commonly called the horizontal line, is produced by the interfecftion of the vanifliing plane FHML with the plane of the pi(5lure HLGR. Third. — The parallel of the eye F M, is a line produced by the interfe6lion of the vanifhing plane with the diredling plane U V F M ; and as this line is the interfedtion of a plane palling through the eye always parallel to the pidure, confequently FM ( 201 ) F M is always pai'allel to the vaiiifliing line H L, and of equal height to it. Fourth. — The directing line U V is the interietftion of any original plane ABDO with the direcSling plane U VFM. Fifth. — The vertical line Q s pafling through the center of the picture s, is the interfedtion of the verticle or upright plane P N J Q with the plane of the pidture ; and P N, the perpendi- cular height of the eye, is the iiiterfedtion of the vertical with the directing plane. Sixth. — The vifual line a; i6, is produced by the interfedtion of the vifual plane P Y C X with the plane of the pidlure, and is therefore the indefinite reprefentation of the original Z X. Seventh. — The dire<5lor of an original line. If any original Z X be produced till it cut the diredting plane U V F M, a line P Y is termed the diredlor of that original line Z X. Eighth. — The radial line *, or parallel of any original line Z X. In whatever degree of obliquity the original line Z X in- terfedts the ground line G R, in the fame degree of inclination * Radial, from px^in^, rabdcs, or radittSt a ray of light. C c will ( 202 ) will the radial Vv cut the vanifliing line HL; for P i; is parallel to the original line Z X. Of PointSy in Perfpeciive^ produced by the Interfeciions of the preceding Lines. As the interfeflions of planes with each other generate or produce lines, fo alfo lines meeting or cutting each other pro- duce points. "Hence the following points in perfpedlive are produced by the interfedtions of the lines M'hich we have now defined. Firft, the point of fight, or the place of the eye ; P is that point where the fpeftator's eye ought to be placed in viewing the picture. Hence, if through the eye P a line perpendicular to the original plane be produced till it cut the parallel of the eye F M, their point of interfed:ion is the point of fight P. Second, the center of the pidure. If from the point of fight P a line be drawn perpendicular to the pidlure, and be produced till it cut the vanilhing line H L, their interfe6tion will be the point j, or that point termed the center of the pic- ture ; {\9-03 ) tiiie ; and the cliilance bet^'een the point of light P, and s the center of the picture, is called the diftance of the piclure ; and the Hne itfelf which meafuies this diflance, may be termed the dire<ft" radial. - -^ * J -if- ■ Third, the vanifliing point. If from the point of ilght V, a line be drawn parallel to any original Z X, and is prodnced till it cut the vanifliing line HL, their point of interfe^Slion <i; is the vanifliing point of the original line ZX; becaufe, if the original line Z X were infinitely produced on the ground pian^ A EDO, its image ZX on the pi6lure would at length vanifli or difappear to the eye P in the point v. The line which mea- fures the diftance between v and P, is the diftance of that vanifli- ing point V ; and the line itfelf may be termed the oblique radial, becaufe its original Z X is oblique to the pid:ure. Fourth, the point of interfecStion. If the original line Z X be produced till it cut the ground line G R, that point i6 where the line G R is cut, is called the point of interfedion : and if the original line Z X be flill continued till it cut the direcff ing line U V, the point Y, where they interfedt, is termed the dire61:- point of that original Z X. Laftly, the point of ftation. If from the place of the eye P, a line be drawn perpendicidar to the ground plane C c 2 at ( 204 ) at N, that point N is the point of ftation, or foot of the fpec • tator. I fliall conckide this fedlion with advifing the reader to make himfelf well acquainted with the preceding planes, lines, and points, before he proceed further : which, if he do, it will enable him to read the fubfequent pages more eafily, and often prevent the trouble of referring to the plates. Add to this, it will make him underftand more readily the problems and ope- rations of both this and other publications on the fubje(5t» SECTION ( 205 ) S E C T I O N II. ^be Affinity and Agreement between Optical Laws and the Prin- ciples of Perfpe&ive demonjlrated — And alfo of the Ufe of the three principal Elementary Planes in the Pra&ice of Draw- ing— Jhozvingy that all that is exhibited by the natural Pojitions of thefe Planes in Fig. 1, may be corre^ly drazvn on any even Surface without their Aid. — Of the various Pojitions of Lines and Planes to the Picture., and of the Principles of Vanijhing Points agreeing therewith^ Of the Affinity of Optical Laws zvith the Principles of Perfpe&ive. In Sedtion I. page 183, it has been fhown that all objedis appear proper tionably lefs as they are farther removed from the eye ; and as the reader is now fuppofed to be acquainted with the planes, lines, points, and terms, which have been ex- plained in the preceding fedtion, I fliall proceed to Ihovv that the rules of perfpedlive agree with optical laws. Thus- ( 206 ) Thus: let G R, Fig. 4, be the ground line, and H L the ho- rizontal or vanifliing line, whofe height above the ground line is equal to that of the eye of the fpe<ftator ; j- is the center of the picture, and s D the diftance of the fpe^lator's eye from the ob- ]c6t3d. Draw dd perpendicular and equal to BD, Fig. i, and as much to the right hand of j as D, in Fig. i, is to e. Then, in Fig. 4, draw the vifual lines ds and l^ s; which lines are to deter- mine the heights of the two original objedts, EC, F G, in Fig. i. Then take the fpaces D C, C G, from Fig. i, and transfer them to Fig. 4, from a to a, and from a to n, on the ground line GR. Draw the lines «, D, n D, cutting the vifual line ds in^^ r; and lailly, from g and ^on the vifual sd, raifc perpendiculars to j- ^; then will g,f, c, e be the perfpedive reprefentations of G F and C B in Fig. i. The analogy between the two figures %vill appear as fol- lows. — In optics, P, in Fig. i, is the pupil, and P e the direct ra- dial or axis of the eye, and equal to the diftance of the firft objed; D B from the eye. In perfpective, D, in Fig. 4, is the fame as P in optics, Fig. i ; and in Fig. 4, J-, the center of the pi6ture in perfpedlive, is the fame as e in Fig. r. Therefore as P ^ in optics is the diretll ray, and the diltance of the firft obj^<fk DB from the pupil P, fo j- D, Fig. 4, in pcrfjxjiflive, is the diftance of the fpedlator's eye from the picture. In optics, if the fecond obje6l C E is removed twice as far from the eye P as the firft I object C 207 ) objedl DB is, its image m v, on the retina, will be little more than half the length ofthe image /;2 of the firflobjecft DB on the retina; and, in perfpediive, Fig. 4, the reprefentation. c e of the fecond obje6t C E, is exadlly half the length of the firft object D B, as Fig. 4 demonftrates, and which coincides with Fig. i ; for obferve, the rays of light P E, P C, coming from the fecond objedt to the pupil P, cut D B, their fe(5lion, in the fame proportion as the vifual lines sd^ sb^ of Fig. 4, cut the perpendicular c e. Hence the fpace 2, 7, on D B, is equal to the reprefentation c e^ Fig. 4 ; and in the fame manner the fpace i, 8, \vhere the rays of light from FG cut the picture DB, is equal to^,/, Fig. 4, the repre- fentation of G F, Fig. I. / Laftly, the reprefentations g /, c e, in Fig. 4, approach to the center j, in the fame proportion as their originals G F, C E, in Fig. I, approach to e, the center of the imaginary plane B D, which is fuppofed to cut the rays of light P C, P G, at 2, i ; for the fpace D 2 and i on Fig. i, is the fame and equal tod, 2, i, on Fig. 4; fo alfo \^ d, <?, Fig. 4, to D e. Fig. i. And hence it may be concluded, that the rays PC, P G, are to their fecftion D ^, Fig. I, as the vifual line d s is to its dividers or meafur- ing-lines D^, D «,, Fig. 4. Before I conclude this head, it will be proper to obferve, that notwitliftanding the general agreement between optical laws o ( 208 ) laws and the rules of perfpedtive, yet in one refpedl there is a difference, for the perfpeclive reprefentation of any object on a plane, is not the fame exactly with the appearance of that object to the eye; and therefore in allufion to this differ- ence, I have, in the preceding page, already faid, " In optics, if the fecond obje<ft C E is removed twice as far ft"om the eye P, Fig. I, as the firft objecl; D B is, its image m v on the retina will be little more than half the length of the image / n of the firft objetfl DB; but the reprefentation 2,7, of CE on a plane D B, which is the fe«ftion of the rays PC, PE, is only half the iength of the firlt objeil DB, as the figure itfelf demon- ftrates." The reafon of this difference is owing to the eye being a fphere, but a picture a level furface or plane ; for the rays PC, P D, cut the arch or fphere K L at 6, 5, in a different pro- portion to what they do on the plane B D, as is plain ; becaufe the fpace D 2, which is the reprefentation of the fpace DC on the plane B D, is greater than the fpace 6, 5, on the fphere K L ; which fpace 6, 5, is the appearance of the fpace D C to the eye ; but the Tpace D 2 is its reprefentation on the pi6ture. This difference, however, decreafes the further the obje<5t is removed from the £ye, for then the rays do not cut the pidture fo ob- liquely ; confequently the reprefentation of the original objecSt on the plane of the picture is more natural, becaufe it has more of the appearance of that real objedt to the eye. Thus : if the x)bje<5t EC be removed back to FG, the rays PG, PF, are lefs 6 oblique ( ao9 ) ■ oblique to the pitflure BD; and therefore the reprefentatioii I, 8, on the pitSlure B D, is nearer to its true appearance o b on the arch K L, than the reprefentation 2, 7, is to its true appear- ance 5, Ti, on that arch; but much more does this difference appear between the firft obje6l B D and its real appearance y, 60, on the arch K L, which yet would be confiderably more if P were removed to Z. Hence the neceffity of chooling a proper diftance for the reprefentations of obje6ls on a pi<fture, that their appearance on the picture may be nearly the fame as the real objedts have to the eye. This will be touched on in its proper place. The difference then between the reprefentation of obje(5ts on a plane and their appearance to the eye, which is a circle, is as the difference of the tangent of the arch, which compre- hends the angle under which the objedl is feen, is to the fub- tenfe of that angle. Thus: let D C be the objedt viewed atP, then will 6, 5, on the arch KL, be the opening or fubtenfe of the angle under which the objedt DC is feen, which meafures four- teen degrees ; and D 2, the reprefentation of DC on the plane BD, is the tangent of that arch 6, 5, which comprehends the angle under which D C, the obje<St, is feen. D d From ( 210 ) From what has been faid on this fubjedl, it is evident that a perfect piffture of objedls, as they appear to the human eye, cannot be dehneated on a plane. It may be done on the furface of a fphere, when the eye of the fpedlator is fup- pofed to be in its center; for then every part of the pic- ture would be equidiftant from the eye, and every ray of light perpendicular to its own furface, as are the rays y P, IT, P, &c. of the fphere K L. None of the rays, in this cafe, could cut the pi6lure obliquely, and confequently no diftor- tion would appear. But though this be the cafe, yet it will not afford any folid objection to the certainty of perfpe(5tive rules adjufted to a plane; for, by the help of light and fha- dow applied in different degrees of ftrength to obje»5ls as they are more or lefs remote from the eye, and by a judi- cious choice of the diftance, a pi(5ture may be drawn on an even furface, fo as to deceive the eye, and produce in the mind fimilar effects with the original or real obje(5ls. 0/ ( 211 ) Of the Ufe of the three principal "^^ Elementary Planes in the Prac- tice of Drawing — alfo fhewing that every thing exhibited by the natural Pofition of thefe Planes in Fig. 2, 7fiay be drawn on an even Surface without their Aid. It is not always underftood, even by thofe who have fome general notions of perfpecStive, how it is that thefe planes anfwer to a level furface, fuch as the paper we draw on ; but, until there be fome conception of this, I will venture to fay that per- fpedlive can never be clearly comprehended. Therefore, that the reader may have a clear view of this matter, I fliall refer him to Fig. 5, Plate XV. in which are fliewn fimilar letters and nume- rals, correfponding with the limilar planes, lines, and points of Fig. 2, as follows : The plane GOBR, Fig. 5, is the original or ground plane GO BR, Fig. 2; alfo the plane GHLR, Fig. 5, is the perfpec- * Elementary, " from the Latin elementum," the firft rudiments or principles of any fcience. Hence, in perfpedtive, the ground plane, the plane of the pidture, and the vanifliing plane, are confidereJ as the three chief elementary planes ; becaufe the firft principles of the art niuft be derived from them. The vertical, direifling, and vifual planes, are alfo termed elementary, as has been fliewn in the firft feflion, but not fo eflential in praflice. D d 2 tive ( 212 ) tive plane denoted by the fimilar letters in Fig. 2; and the plane FHLM, Fig. 5, is the vanifliing plane FHLM, Fig. 2. If, in Fig. 2, a line be extended from P to s, from s to Q, and from Q to U, that line will meafure the length of all the three planes in Fig. 5, as from P to U. Thus the ground plane, the perfpedtive plane, and vanifhing plane of Fig. 2, are fuppofed to be ftretched out of their natural pofition till they become an even fur face, as in Fig. 5. The line GR, in Fig. 5, is therefore the interfedtion of the pidlurc with its original plane, as in Fig. 2 ; and the line HL, Fig. 5, is the vanifhing hne produced by the interfedtion of the vanifliing plane with the plane of the pic- ture, Fig. 2. The line FM, Fig. 5, is the parallel of the eye, denoted by thefe letters in Fig. 2. And laftly, Q j. Fig. 5, is the vertical line Qs, Fig. 2, which is produced to P, in Fig. 5 ; on which is placed the diftance Pj of the fpedtator's eye from the pidture, as P s, Fig. 2. Thefe things being underftood, proceed to draw the plan of the cafe of drawers on the ground plane GO BR. Thus: from Fig. 2, take the fpace T, equal to the diftance which the drawers are placed from the pidlure. Transfer this fpace to Fig. 5, from Q to /, and draw the line i, 3, parallel to G R ; be- caufe I, 3, in Fig. 2, is parallel to the plane of the pidlure. Ex- tend ( 213 ) tend the compaffes from i to 3, and from T to w, of Fig. 2, for the length and breadth of the drawers, and make the plan on Fig. 5, the fame. In Fig. 5 produce the line 8, 3, and 2, i, to G R, at the points 10 and 12, anfwerableto 10 and 12, Fig. 2. Draw then the vifuals 10, J, 12, J-, Fig. 5, correfponding with 10, J-, 12, s, Fig. 2, on the plane of the pidture. Take then from Fig. 2, the perpendicular height T y of the drawers, and place this from 10 to ^, and from 12 to «, Fig. 5. Draw then the vifuals ds, as, anfwerable to the fame letters in Fig. 2. Next, from the points i, 3, 8, 2, draw lines tending to the point P, which will cut the vifual lines at I, 3, in the fame manner as the rays i, P, 3, P_, cut the vifuals 10, s, 12, s, at i, 3, Fig. 2. In Fig. 5, from i, 3, raife the perpendiculars i, 5, 3, 7, cut- ting the vifuals ^, s, a, s, at 7, 5, in like manner as the rays 5, P, 7, P» Fig- 2, cut the points 5, 7, on the plane of the piaure. Draw then from 7 to 5, Fig. 5, a line parallel to I, 3, which will determine the height of the draMers; and for the apparent breadth of the top, raife a perpendicular^-, 6, from. g, the point where the line 8, P, cuts the vifual 10, s, and the point 6 will determine the apparent breadth of the drawers ; in the fame manner as the rays P, 4, P, 6, cutting the vifuals ^, j-, 3, s, ati ( '214 ) at the points 6, 4, determine the reprefentation of the top of the drawers 5, 7, 6,4, at the correfponding points on the plane of the pidlure, Fig. 2. By thefe operations it is nianifeft that the reprefenta- tion of the drawers in Fig. 5, where the planes are llretched out till they become an even furfece, is the fame in all its parts as the image or reprefentation of the cafe of drawers on the plane of the pi(5lure Fig. 2, where all the planes are in their natural pofitions. This would follow from a procefs of geometrical reafoning ; but, perhaps, it would be too tedious to the reader, and a deviation from the profeffed plan of this treatife ; and, therefore, I Ihall only recommend to him, to apply the com- paffes to each reprefentation in the different figures, by which he will perceive the equality of parts in both ; and, if to this be added a little refle<5lion on the preceding operations, I have not the leaft doubt of its being underftood. Of ( "5 ) Of the various Pofitions of Lines and Planes to the PiSfure, and to the Ground Plane — alfo of their Reprefentation on the Pic- ture agreeing therewith, and of their various Modes of Fa- nijhing. The original line Z X, in fig. 2, is oblique to the picture, and is therefore treated in a diverfe manner from the lines in the cheft of drawers, which are all parallel and perpendicular to the picture, or parallel to the ground plane and perpendi- cular to it.. Cafe I. — When any line i, 3, Fig. 2, is parallel to the pic- ture and to the ground line G R, its reprefentation is parallel alfo. This is felf-evident by infpeding the figure. Cafe 2. — Lines in the aforefaid pofitions can have no va- nifhing line or point in the picture, becaufe if infinitely pro- duced would never cut it ; that is, the lines i, 3, and G R, Fig. 2, would never meet in a point, however far produced, for lines truly parallel can never cut each other. Cafe 3. — The reprefentations of lines originally parallel to each other and to the pidhire^ are parallel to one another oni ( "6 ) on the picture. Thus : the lines i, 3, 5, 7, 4, 6, Fig. 2, arc all pa- rallel to each other and to the pi<ftme; therefore their repre- fentations i, 3, 5, 7, 4, 6, on the pi6:ure, are all parallel to one another, as is felf-evident by comparing thefe with their cor- relponding lines in Fig. 5. Cafe 4. — If any original line 1,5, Fig. 2, be perpendicular to the ground plane, its reprefentation will be peri>endicular to the ground line G R ; wherefore the reprefentation of the ori- ginal 3, 7, or any other in the like pofition, fituated any where on the grovuid plane, is perpendicular to the ground line G R. Hence the correfpondent lines 3, 7, i, 5, Fig. 5, are drawn per- pendicular to G R, the ground line. From the above theory it may be concluded, that the re- prefentation of a geometrical fquare or parallelogram *, is a ge- ometrical fquare or parallelogram, if it be fituated in a plane parallel to the pi6lure. Hence IK, L M, Fig. 6, is the true re- prefentation of the original fquare AD, BC, which is in this pofition. Cafe 5. — All lines perpendicular to the pidlure, have their yanifliing points in the center of the pidture. * Sec its definition in page 44, and its figure Plate II. 6 The ( 217 ) The lines 5, 4, 7, 6, of the ends of the drawers, are perpen- dicular to the pi6ture H L G R ; confequently their reprefenta- tions 5, 4, 7, 6, on the pidliire, appear to terminate to a point at s, the center of the picture. Wherefore, in reprefenting the top of the cheft of drawers at Fig. 5, z^* « is made equal to the length 5, 7, Fig. 2 ; and from ^ a, Fig. 5, lines are drawn to the center j-. Hence the reprefentation of a geometrical fquare, fituated in any plane perpendicular to the picture, is a trapezoid, as IK, LM, Fig. 6; that is, two of its fides, IK, LM, are parallel, and the other two, K L, I M, not fo -. In whatever pofition an original plane may be in with re- fpe<fl to the ground plane, if it be but perpendicular to the pi6lure, the reprefentation of a geometrical fquare in that plane will ftill be a trapezoid. If the planes be above or below the horizon, its appearance will be of that figure. Thus, in Fig. 3, a, by o^p, is the reprefentation of a fquare fituated in the ground plane, which is certainly perpendicular to the pi6lure, if the picture be perpendicular to the ground; as N17, a fedlionof the picture, is upright to (7/^, one of the fides of the fquare : <:/isalfo the reprefentation of a fquare, fituate in a plane raifed above the * See its definition page 44, and its figure Plate II. E e ground ( 2i8 ) ground i>lane, b\it parallel with it, and therefore perpendicular to the pidlure in this cafe; alfo e f\% the reprefentation of the fame fquare, lituate in the plane of the horizon, which is a plane equal to the height of the eye, as the plane F M H L, Fig. 2. M'lierefore in this plane the fquare does not appear, for it vanifhes into one right line, as e i. But if thicknefs be attri- buted to the fquare, as denoted by the double line, then, by the help of fhadow, two of its fides may be feen, as ^ i, i, 2 ; but obferve, both the fides are in one right line. The fquares^' h, Ik, are in planes above the horizon, ele- vated nearly as much as the other two a b, c i, are below it; their appearances are therefore trapezoids of nearly the fame dimenlions. And it is alfo evident, fince all thefe fquares arc fituate in planes perpendicular to the picture whether above or below the horizon, they muft have their vanifliing point in the center of the pidlure s ; and, as they are all parallel to the ground l^lane, their common vanifhing line will be H L. Cafe 6.— If a geometrical fquare be lituated in a plane in- clined in any angle to the ground plane, whether it be above or below the horizon, provided the plane be confidered perpendicu- lar to the picture, its reprefentation will be, as before, a trapezoid; and likewife its vanifliing point will be in the center of the pic- ture. Thus, in Fig. 8, No. 1, ADBC is the reprefentation of a geometrical fquare in a plane A E P O, inclined to the ground plane ( 219 ) plane equal to the angle n AD. Now it is evident, that the fqiiare will incline to any angle, by fiippofing it to revolve on its center A C in the arch unk; for the fide D B of the fquare may be prefled to t ^ or o u^ or to any point in theie arches, without altering its pofition to G R, the ground line or fe6lion of the pi6ture ; therefore, wherever the fide of the fquare D B is in thefe arches, it will ftill vanifli to s, the center of the pic- ture ; and its appearance will be a trapezoid : for u o, D B, .^ f, are all parallel among themfelves, and to r s, which is perpen- dicular to the picture. For the fame reafons the other fquares above the horizon, though inclined to the ground in different de- grees, and in different directions, have the fame vanifliing point. Cafe 7. — All lines oblique to the pit^ture, but parallel to the groimd plane, having their vanifliing points fomewhere in the horizontal line H L, Fig. 2 ; but not in the center of the pidlure, as in Cafe 6, when the line is perpendicular to the pidtiu^e. Alfo if oblique lines are parallel to each other, they all have the fame vanifliing point. The original line Z X, in Fig. 2, is ob- lique to the picture, and its vanifliing point is at v in the va- nifliing line H L, not at s, the center of the pi(fture; for a line drawn from the eye P, and produced till it cut the pi<Sture at Vy in a parallel direcftion to Z X, is the vanifliing point of that ori- ginal hne Z X. Wherefore, in Fig. 5, where the elementary planes are ftretched out to an even furface, draw the original Ee 2 ZX ( 220 ) Z X inclined to G R, in the angle which it is fuppofed to be in to the pidlnre in Fig. 2. Produce X Z till it cut G R at 14 in Fig. 5 ; then lay the diftance of the eye from the picture on the vertical line at P, and from P draw P v parallel to Z X ; then will v be the true vanifliing point to the line Z X, upon the fame prin- ciples that ^', in Fig. 2, is the vanifliing point to Z X in that figure. If a number of lines oblique to the pidlure be parallel to each other, they will all have the fame vanifliing point ; for the fame reafon as a number of lines perpendicular to the picTture have but one vanifliing point in the center. Therefore, in Fig. 9, Plate XVI. the geometrical fquare i, 2, 3, 4, having its fides ob- lique to the pi(5lure, the fides which are parallel to each other are drawn to one vanifliing point. The fides db^c a^ are originally parallel to each other, for they are the reprefentations of 2,3,1,4, of the original fquare, wherefore they vanifli into one point at V. In like manner, and for the fame reafon, the fides b a^dc^ vanifli at V. It is evident then, that the reprefentation of a fquare, having its fides oblique to the picSlure, is a tra- pezium * ; that is, none of the fides are parallel to each other. * See its figure Plate II. and its definition page 45. Cafe C 221 ) Cafe 8. — When a fquare is fituated in a plane perpendicular to the ground, but oblique to the pidture, only two of its fides will vanifli to a point, as B C, A D, No. 2. The other fides, A B, DC, can have no vanifiiing point; becaufe they are perpendi- cular to the ground, and parallel to the pi6lure. See Cafe 2, page 215. Its reprefentation is therefore a trapezoid. And becaufe the fquare is not perpendicular to the picture, its vanifliing point is not in the center s, but in fome other point v in the horizon, according to the angle which the original fquare makes with the pi6lure, or with its interfedtion. Thus MA/ is the angle which the fquare A B, DC, makes with the interfedlion, or ground line G R ; or, in other words, it is the original pofition which the fquare ftands in to the pi6ture. Hence v d being parallel to M A, it forms the fame angle to the vanifliing line H L ; and being drawn in this dire(5lion from the place of the eye d^ and produced till it cut H L at "u, confequently v is its vanifliing point. Cafe 9. — If a fquare be fituated in a plane inclined to the ground plane, and its interfedtion with the pidture be parallel to the interfedlion of the ground plane with the pidlure, as AF, No. 3, then the vanifliing line of that plane wiU be parallel to the ground line G R ; and two of its fides, A N, F O, may be confidered as perpendicular to the picture ; but the other two fides, ( 222 ) fides, A F, N O, are really parallel, and therefore have no vanifli- ing point in the vanifliing line H L. See Cafe 2, in page 215. The fides A N, F O, are confidered perpendicular to the picture ; becaufe, it is evident, that the fquare may be fuppofed to revolve on the fide A F, and be preffed or moved to 8, 10 ; which fhow the angles of the fame fquare in a plane ftri<5tly perpendicular to the pi<Slure, and therefore its fides 11, 8, 12, io» have their vanifhing point in the center j-. See Cafe 4, in page ai6. Wherefore, as the fquare may revolve on A F, as a table top hinged at the front, and rifing to any angle from its frame, its vanifhing point will rife on the verticle line s d, in proportion to that angle. Hence S is the true vanifhing point of the fquare A F, N O, making the angle F A 6 with the ground plane. Cafe 10. — If a fquare be fituated in a plane of the above kind, having its fides oblique to the pidture, every thing will be confidered the fame as in the foregoing cafe, only the fides will vanifli to two points in the horizon ; neither of which can be in the center j, nor in any part of the vertical line s d ; be- caufe the fide A B, Fig. 10, of the original fquare, is not per- pendicvilar to GR. But, as the interfedion of this inclined plane with the pidlure is parallel with the ground plane, as in 7 Cafe ( 223 ) Cafe g, the vanifliing points will rife in a perpendicular direc- tion above the common vanifhing line H L, in proportion to the angle which the inclined plane makes with the ground plane. Hence ^' t? on the new horizontal line h /, are placed per- pendicular to V V in the common horizon H L ; which points V V would be the true vanifliing points of the original fquarc A B, B C, were it reprefented upon the ordinary ground plane ; or, in other words, if it were reprefented in a plane perpendi- cular to the pidiure, and parallel to the ground plane. Cafe II. — If a fquare A DBG, Fig. ii, be fituated in a plane oblique both to the ground plane and to the pi(Sture, its vanifliing line will be in an angle to the common horizon H L, in proportion, to the angle which the inclined plane makes with the ground. For, as the original plane in this cafe is inclined both to the ground and to the pidture, confequently its inter- fedtion with the pi(Sture will be oblique to the interfe6tion of the ground plane with the picture. Cafe 9 has a horizontal vanifliing line, though it fuppofes the original plane to be in- clined to the ground ; but as its interfetSlion is parallel to the ground line, fo its vanifliing line is parallel alfo. In the cafe before us, the original plane has an oblique interfedion with the ( 224 ) the picture, and therefore its vanifhing hne is obUque to the horizon alfo; which, perhaps, may be better iinderftood by No. I, Ihowing the fame fqnare in the fame polition, confidered as the top of a table viewed angle-ways, whofe top is fuppofed to be rifing on its hinges at A C in the angle ii A K. Its vanifli- ing line is therefore v V, found by drawing M V, making an angle with the horizontal line H L, equal to u A K, the angle which the inclined plane makes with the ground. Or the va- nifhing line maybe found as in Fig. ii; by drawing t^M, cut- ting O OT, which is a line perpendicular to the horizon ; from the meafuring point m, draw M V parallel to the horizon, cut- ting V P at V ; then will the line v V be the true vanifliing line as before. The line A X is confidered as the interfe6lion of the inclined plane, and is therefore drawn parallel to v V, the vanifliing line ; for, in perfpedlive, it is a univerfal theorem, according to Dr. Brook Taylor's fyftem, that the vanifliing line, interfedtion, and dire6ting line of any original plane, are pa- rallel to each other ; alfo, " the vanifliing points of all lines in any original plane, are in the vanifhing line of that plane." See his Sixth and Seventh Theorems. Wherefore the line A X is to f V the vanifliing line, the fame as the ground line GR is to the horizontal line H L. Thefe, and the other lines which I have hitherto palTed over ( 225 ) over unnoticed in the various cafes, will be explained in the different problems belonging to each particular cafe, and there- fore I deem it unneceffary to fay more on them at prefent. .,., SECTION III. Qqntaining Problems in Ferfpeciive^ folved according to the pre- ^i feeding Principles and Cafes — applied to the Methods of drawing \s\reuiangular Superficies and Solids in different Pojitions to the ■ Pi&ure. — Alfo^ how to draw Vifual Lines ^ tending to vanifhing Points^ out of the Pi&ure ; and how to reduce the Point of Dif- tance to any Proportion^ fo as to bring it within the Limits of the Pi&ure. In the methods of inftrudlion generally made ufe of by moft of thofe who have written on this fubjedt, it is common for them to begin with finding the reprefentations of points and lines, proceeding afterwards to fuperficies and folids. To me, however, it appears an unneceffary prolixity, ef- pecially it would be fo to the perfons for whom this treatife is chiefly intended. For to go through all the problems neceffary for points and lines as they may be differently fituated to the ground plane and pidure, and alfo to fhow how thefe lines are to be meafured off according to any given length, would take Ff up ( 226 ) up as many plates and pages of letter-prefs as would be fufli- cient to explain the fuperficies of figures of which thefe lines are the boundaries. Befides, it is prefumed that the general readers of this work will underftand the various pofitions of lines, and how to meafure them off, according to their given lengths, better when they are connefled with fome figure, than when thefe fame lines are confidered abftra<Stedly. And, in general, it may be faid, that when perfons fet about drawing, it is not to reprefent a line or a point nakedly, but to draw the perfpe6tive appearance of fome figure bounded by lines and points ; which, when performed, muft of courfe include every thing requifite to the reprefenting or meafuring of a bare line. Therefore, in finding the reprefentation of a geometrical fquare, for inftance, the problem for this will teach us both how to find the points of its angles, and at the fame time how to reprefent and meafure a line equal to the fides of the given fquare, or any other figure of that nature. For thefe reafons I omit points and lines, and proceed to the firft problem, which is Prob. -V/'// /'^- - .i't///(//fS /// i////tnv// Jt'sz/rt'. J'!<itr IS. r.Sheraeon Z>f/ Fui/i/iied ur r/if Arc directs- /r G T^rry J/rii' ^. z-^« ./.Bijr/rffS'-*i//>- ( 227 ) Prob. I. Fig. 7. Plate XV. To reprefent a Geometrical Square lying on the Ground^ having tzvo of its Sides parallel to the Figure, and the other two per- pendicular to it. Operation. — Draw the ground line GR, and draw HL for the vanifhing line, whofe height from the ground line is fuppofed to be equal to the height of the fpe6lator's eye. Make s the center, or that point in the picture which is directly op- polite to the eye when the pidture is viewed. Make d the dif- tance of the eye from the picture, anfwering to Pj-, in Fig. 2, Plate XIV. In this manner the paper or canvafs we draw on is prepared for delineating objedts in the above lituation. The next thing to be confidered, is the feat of the object in the pi6ture ; that is, how far the fquare, for inftance, is to be placed to the right or left of the center j, or whether it is to be dire6tly under the center, and how far removed back from the pi6ture. Thefe being fixed on, lay down C A equal to the fide of the fquare to be reprefented, and draw the lines C J", A j-, termed vifual lines. Determine then how far the fquare is to be removed from the pidlure, which in this example is equal i 2. F f 2 Draw ( 228 ) Draw from 2 a line to the point of diftance d, cutting the vifu- als Cj, A J, at B and A. Laftly, from thefe points of interfec- tion at B and A, draw the hnes AC, B I, parallel to G R, the ground line, and the reprefentation will be completed as re- quired. Obfervations. — The fides C B, A I, of the fquare, are per- pendicular to the pidlure, and therefore, by Cafe 5, page 216, they muft vanilh in j, the center of the pi6lvire. The fides C A, B I, are confequently parallel to G R, the interfedtion of the pic- ture or ground line ; wherefore, by Cafe r, page 215, they are the reprefentations of original lines parallel to the picture ; and being parallel, they can have no vanifliing point. Prob. II. Fig. 7. Plate XV. To find the Reprefentation of a Square perpendicular to the Ground^ and alfo to the Fi&ure. The picture being already prepared in the foregoing problem, the ground line and vanifhing line remain the fame ; alfo the point of diftance and the center s are the fame. And it fhould be obferved, that G R is the ground line, and H L the horizontal line in every example. Alfo s denotes the center of the ( 229 ) the pidlure, and d the diftance ; therefore, in future, the expla- nation of thefe may be omitted, and we may proceed as follows : Operation. — Draw the perpendicular A D equal to the fides of the original fquare, and draw the vifuals D j, A j. Then, on the ground line G R, lay on a fpace from i to C equal to the diflance of the fquare from the front of the pidlure. Make C N equal A D, and draw C tf, N ^, cutting the vifual A J" in I and M. Laftly, from I and M raife perpendiculars to K L, and the fquare will be reprefented as required. Obfervations. — The fides IK, M L, are perpendicular to the ground; wherefore, according to Cafe 4, page 216, they are the reprefentations of lines originally perpendicular, as AD; and being perpendicular to the groimd, confequently they are pa- rallel to the pi(fture, and therefore can have no vanifhing point. But the fides KL, IM, are perpendicular to the picture; there- fore they vanifh to s^ the center. Prob. ( 230 ) Prob. III. Fig. 6. Plate XV. To reprejent a Square Jlanding upright on the Ground^ but parallel to the Pidiure. The grovind line and horizontal line, &:c. remaining as in the preceding problem, proceed to the operation. Draw ADBC a geometrical fquare on the ground line. Draw the vifuals A j", Dj, Bj, Cj; then lay on a fpace AN on the ground line equal to the diftance which the fquare is fuppofed to be from the picture. Draw N J cutting the vifual A j in I. From I draw I M parallel to A C. Draw I K, L M, perpendicular to A D, C B. And, laftly, draw K L parallel to D B ; then will the fquare I K, LM, be the reprefentation of the original fquare ADBC, as propofed. Obfervations. — The vifual rays Aj-, Dj, Bj-, Cj, form a pyramid *, whofe bafe is a geometrical fquare ADBC, and whofe vertex is J", the center of the picture. If this pyramid have a fedtion parallel to its bafe, it muft be evident to every one, that the fecStion will produce a geometrical fquare. The * Sec its definition page 9^, and its figure Plate VI. reprefentation ( 231 ) reprefentation I K L M is a parallel fedlion of the pyramid of rays iffuing from each angle of the original fquare ADBC, and therefore IKLM, the fedlion, is a geometrical fquare. See the conclufion drawn from Cafe 4, page 216, in which we fay, — ^' That the reprefentation of a geometrical fquare or parallelo- gram is a geometrical fquare or parallelogram, if it be fituated in a plane parallel to the pi(5lure." Prob. IV. Fig. 8. Plate XV. To reprefent a Square fituated in a Plane inclined to the Ground^ and perpendicular to the Figure. A OPE may reprefent the inclined plane, which is merely to affift the imagination, or to convey what is to be underftood by the fquare ADBC, No. i. being in a plane inclined to the ground. Operation. — On GR, the ground line, draw the femicircle u n k^ whofe radius muft be equal to the lide of the original fquare. Draw nh perpendicular to the ground line; then make « A D equal to the angle of inclination which the original fquare has to the ground. Draw then, as before, the vifuals A j-, D j-, to the center s. Let d, near L, on the common horizontal line 7 HL, ( 232 ) H L, be the diftance as in common; draw the line tid cutting thevifual Une A j- in C. From C draw CB parallel to AD, then will A D C B be the reprelentation of a geometrical fquare, Situ- ated in a plane inclined to the ground, in an angle of twenty- three degrees. Method fecond. — Let G i, R i, be the interfe<5lion of the in- clined plane with the pidlure ; or, in other words, let it be con- sidered as a new ground line, and turn the plate till this line come into the fame fituation with the eye as the old ground line GR appeared to be in when the plate was upright. This will make every thing in this fecond method appear quite plain, I prefume, and will fhow that it is as ,eafy to reprefent a fquare in a plane inclined in any degree to the groiuid, if it be per- pendicular to the pi6lure, as it is to reprefent one lying on the ground, having two of its fides perpendicular to the picture. The plate being placed to the eye as above inentioned, draw a new horizontal line b /, //, parallel with G i, R i, paffing through the center s. Make s d on this new horizontal line equal s don the old one H L. From D lay down the fide of the fquare D A, and draw the vifuals A s and D s. From A draw A d, cutting the vifual D j- in B. Make B C parallel to A D, and the reprefentation will be as before. In No. 2 the fame fquare is inclined to the other hand ; but the operation is ftill the fame, when the new ground line G 2, R 2, is drawn, and when a new horizon ( 233 ) horizon, h^, lo., is drawn parallel to it, paffing through the center j-, d near b 2 will then be its diftance, or d near li will do, for they are both the fame to the fquare No. 2 ; fince both the diagonals of the fquare, if produced, will tend to each point of diftance, as is evident from infpe<Slion. The fquares No. 3 and No. 4 are reprefented above the horizon ; but as they are con- fidered in planes perpendicular to the pi6ture, this makes no difference in their reprefentations, for their perpendicular fides vanilh in j, the center, and the operation is the fame above as below the horizon in all refpe(5ls. As I have marked the ground lines and vanifhing lines to each fquare, diftinguifliing them by the fame numeral that the fquares are marked with, I think it imneceflary to go through the operations, as it wpuld only be repeating what has been faid on thofe below the horizon. See Cafe 6, on Fig. 8, No. i, in page 219. Obfervations. — From what has been faid on Fig. 8, it is evi- dent that the foregoing problem may be applied to ufefid pui*- pofes in reprefenting different pieces of furniture ; and that which has been frequently done at random, for want of know- ing better, may be done with great eafe and accuracy. For inftance, the rifing defks of the library table, Plate XXX, are reprefented by this problem. The two femicircles fliew that the delk, raifed to any pitch, will ftill be within thefe arches, G g which ( 234 ) which are the boundaries of the defk, as it paffes round on its hinges. Prob. V. Fig. 9. Plate XVI. To reprefent a Square fituated in a Plane inclined to the Groundy and to the Figure, when the Interfeclion of the inclining Plane is parallel to the Ground Lin.e\ or when its Interfe&ion is in the Interfe^i9n of the Ground Plane with the Pi&ure. In this cafe the common ground line G R is the interfec- tion of the inclined plane with the pidlure ; and a line, S P, produced parallel to G R will be the vanifhing line of this plane. Operation. — Let H L, the common horizon, be drawn as ufual ; and let s be the center of the pidture. From j to jf) is the diftance of the eye from the picture. Take in the com- paffes, A F, equal to the fide of the fquare, and with it fweep the arch q r from p ; then from r to ^, on the arch q r, lay on the degree of inclination which the original plane has to the ground ; and draw p q produced till it cut the vertical line sd'xvi S ; then will S be the vanilhing point of the fquare in the in- 6 dining X'.'/i/ . /V, Sgnnrrx n/ iNi:/i//i',l /i/u/ir.s F/r//r^ J^j. T.-r/u-mA-u /?r, /lM///,;f ti.i-r/ie.li-f(/irfrn />v /r. TfiTi/. .'/<ir if"jjin ( 235 ) dining plane, for the fame reafon as s is of the fquare ii, 12, 10, 8, on the level ground. Make SP equal to sp, and P will be the point of diftance to the inclined plan''. Draw the vifuals A S, F S, and from A draw A P, cutting the vifual F S in O. Laftly, draw O N parallel to A F, and the reprefentation of the fquare will be found as propofed. See Cafe 9, page 221. Obfervations. — The vifuals A S, F S, may be cut by another method to the fame effedt. Thus : draw the line 5 6 parallel to Sp, and take the fide of the original fquare and place it from A to 5. Draw from 5 a line to p, the diftance on H L, and it will cut at N, as before. The truth of this will appear by com- paring No. I with No. 3. At No. i draw G R for a ground line, and perpendicular to it draw A j-, a fe6tion of the pidture. Lay on, from A to s, No. i, the height of the common horizon ; that is, from A to j- on the perpendicular line AB s, Fig. 9. From s, the center of the pidlure at No. i, draw sp equal s p the diftance at Fig. 9. Make A N, the inclined plane, of equal angle to g p r, the angle which the original plane makes with the ground. From A to N, No. i, lay on A F equal to fide of the fquare No. 3. Lay the fame from A to G, No. i. Laftly, draw Gp, N/), cutting the picture at n and 8. Take, in the com- paiTes, the fpace from A to «.at No. i, and lay it from 9 to N at No. 3, and it will be feen that they are equal. In the fame manner take A 8 at No. i, and lay it from 9 to 8 at No. 3, and Gg 2 it ( 236 ) it will be found that they are ecjiial. This fully (lenionftiates the truth of the reprefentatioii of the fquare A F, N O ; for, be- yond all difpute, ;?, at No. i, fhows how much the fquare on the inclined plane rifes on the pi6ture ; and 8, at No. i, as cer- tainly fliows how much the fame fquare lying on the level ground rifes ; and fince they both coincide with their repre- fentations at No. 3, there can remain no doubt but S is the true vanifliing point, and P the true point of diftance. N. B. This problem is of ufe to reprefent any table top hinged at the front, and rifing by a horfe behind to any pitch. Prob. VI. Fig. 9. Plate XVI. To find the Reprefent at ion of a Square lying on the Ground^ having its Sides oblique to the Pidiure. Operation. — Draw the plan of the fquare propofed, as i, a, 3, 4, in any angle to the ground line G R, as may be required. Produce the fide i 4 till it cut the ground line at k. Alfo pro- duce the fide i, 1 till it cut at i 4. Let s be the center of the pi6ture as ufual, and draw s d perpendicular to H L. Let d be the diftance of the eye from the pidlure. From d^ draw dN pa- rallel ( 237 ) rallel to i, 2, one of the fides of the fquare. From d., draw dv at right angles to ^V, then will V-u be the true vanifliing points of the fides of the fquare ; for the line f/ V is parallel to the fide I 2, and dv \% parallel to 1,4; wherefore vN are the true va- nifliing points. Hence, from i 4, and from 3, draw right lines to V, and from k and 3 draw lines to v ; and where thefe lines cut each other at 4 b^ a, c, will be the reprefentation of the ori- ginal fquare 1, 2, 3, 4, as required. Method fecond. — To draw the fame fquare without the trouble of a ground plane. Operation. — Every thing remaining as before, extend the compafles from v to d, and lay v d to m on the horizon ; then will m be the meafuring point to the vifuals 3, v, k, v. Make d 13 on the ground line equal to the fide of the fquare. From 13 draw a line to m, cutting the vifual ^v 2it b. From b draw b V, cutting at a, as by the firfl method. The angle of the original fquare being brought into the pi6ture at 3, a line from 3 to V finds the other fide dc^ without any further trouble. Obfervations, — The truth of this problem will appear from what has been faid in Cafe 7, p. 219, which I would advife the reader ( 238 ) reader to examine. And I would further remark, that if vifual rays be drawn from each angle of the original fquare i, 2, 3, 4, to the vertical line s d, they will cut at d, a, c, as in the preced- ing methods. The rays from Z X to P, in Plate XIV. Fig. 2, are the fame to the original Z X, as the rays id, ^d, are to the fide of the fquare 1,4, in the figure before us. For c a, in this figure, is the reprefentation of i, 4 — and z, x, on the pi(Slure in Fig. 2, Plate XIV. is the reprefentation of Z X. Prob. VII. Fig. 9. Plate XVI. 7b Jind the Reprefentation of a Square fuppofed to be Jituated in a Plane perpendicular to the Ground^ but oblique to the Fi&ure, For this problem, the picture being completely prepared as for the preceding one, the operation will be extremely con- cife, as follows : Operation. — Raife a perpendicular line A B, No. 2. On the perpendicular A B lay the fide of the fquare from A to B. From B and A draw vifual lines to v, the vanifliing point ; found as before. From A, lay down the fide of the fquare to / ; and from / draw im, cutting the vifual line A v in D. Lafl:ly, draw D C parallel ( 239 ) parallel to AB, and the reprefentation will be found as required. See remarks in Cafe 8, page 221. Prob. VIII. Fig. 10. Plate XVI. To find the Reprefentation of a Square having its Sides oblique to the Fi&ure^ fuppofed to be in a Plane inclined to the Ground^ as in Problem V. Observations. — This problem differs in no refpedl from the fifth, except what relates to the fqiiares reprefented in thefe inclined planes. In the fifth problem, the fquare in that in- clined plane, having two of its fides parallel to the pidlure, the others of courfe vanifh in S, perpendicular to j-, the center of the pidture. In this problem the fquare reprefented in the in- clined plane has its fides oblique to the pi6lure, and therefore they vanifli to two points in fome new vanifliing line, h /, pa- rallel to the common one H L ; becaufe the interfedtion of the inclined plane is parallel to the ground line. Operation.— Draw, as ufual, G R the ground line, and H L the horizon. Let s be the center, and d the dillance of the pidture. Draw A B, one fide of the original fquare ; make ( 24° ) make d V parallel to A B, the fule of the fqiiare ; and draw J, V L, at right angles with ^V, then will V, V L, be tlic vanilhing points of the fquare 4, /), 5, 6, on the level ground. MakeA^M equal V i^, and LVw equal LV^; then will 111 and M be the meafuring points of the vifuals tending to V, V L. Thus far the pidlure is prepared only to rcprefent the fquare on the level ground ; therefore we muft proceed to find the vanifliing line, points, and meafuring points, of the inclined plane, thus : — Draw perpendiculars at pleafure from V, and VL. From M tlraw M i', in an angle to V M equal to the angle which the inclined plane makes with the ground. Through v draw h I parallel to H L, cutting the perpendiculars V ^' at v ; then will 1? i; be the vanifliing points fought. Make v n equal v M, and n will be the meafuring point fought. Draw then the vi- fuals 4 V and 4 ^' /. Make 4, 0, 4, r, equal to the fides of the ori- ginal fquare B A. From draw ;z, cutting at i; and from r draw r/, cutting at 3. From 3 draw 3 1;, and from i draw ivl^ interfedting at 2 ; then will i, 2, 3,4, be the reprefentation of the fquare propofed. Obfervations.— The line /B pafles through the diagonal of the original fquare, whofe fide is A B. Draw from d^ the difiance, a line parallel to B /, cutting at g on the common horizon. From 4 draw a line to g, and it will pafs through the diagonal of the fquare J /6./'/ Z S<fuari-s i/i we///?/"// p/tines . JPlaff ly. _ J 5 \ ""'^ y 7 1\' A^ \ X \\ \ / \> y: \\ ^r ___^/ _\_^ X / / \ /I ' \ / ' \ y^ \ / / ' If ' \ y^ /A '/'^ \>r\ ^^ <f/^- \ / / \ / '-^ K^''''^^ .Py- — ^ ^^^^ \ /y\ / ' H *n 2^ """^ — -^^ P Z 9^' ~^ y^y^^ ^ -••="""""'7' "^^ id Ji V 1 / ^,,,-'^ ^^ ^===*JV^ W' \ ^ ^;;;[^ jf ^^'^^ / ', 1 i'-'X " ~^~^-~^^ I. / ^^ ^^\ ^^^^^^^^B^^^^fe^E^ ^-""^^X./ ^^;^ M^m \. j0.''' - # '. ^jr TSIieralonnel. J^li/7t£ti aj- the Act </ireots, by (r. Terry. Mav rj!-''t^^2 J.Barhw Scu^. ■( 241 ) fquare 4/>, 5, 6, lying on the level ground. Draw from g, a per- pendicular to g on the new horizon b L From 4 draw a line to the uppermoft g^ and the line will pafs through the diagonal of the fquare reprefented on the inclined plane ; which is a clear demonftration of the truth of the whole. The truth of the method may be proved, alfo, by drawing a line from A to D, the diftance laid on from the new hori- zon bl\ for the line cuts the vifual at i, as in the other method. Prob. IX. Fig. ii. Plate XVII. I'o find the Reprefentation of a Square^ fituated in a Plane oblique both to the Ground and to the Pi&ure.. ^ This figure may, to the workman, appear intricate and perplexed ; but he ought not to be difcouraged at the fight of an afTemblage of lines, till, after having made a reafon- able attempt to underfland them, he finds , it not eafily at- tained. But it is to be noticed, that there are feveral more lines than what are abfolutely neceiTary for reprefenting the fquare fimply confidered ; becaufe I have fliown clilFerent me- thods to efFedt the fame thing; and becaUfe the' whole procefs is fhown from firfl to laft, that the reader might have a clear H h underftanding ( 242 ) iinderftanding of a problem really ufeful, but rarely known amongft workmen, and even not amongft painters. Operation. — Draw G R, the ground line, and II L, the ho- rizon, as iifual ; and make s the center of the piiSlure. Draw s d perpendicular to H L ; and let d be the diftance of the pic- ture. Make the angle dv s equal to the angle which the fquare in the inclined plane makes Avith the pidture; and draw fi?P at right angles x.o dv\ and make v m owWL. equal v d. Draw at pleafure mMo perpendicular to the horizon. Make vM to in- cline in an angle equal to that which the original plane makes with the ground. Draw M, V x parallel to the horizon ; and from V .v, draw V x, i;, which will be the vanifliing line of the inclined plane. From the center j, draw s S, dx perpendicular to the va- nifliing line -y, V x. From s, draw a line to d j, parallel to t; S Y X. Extend the compafTes from S to d i, and make S, d x, equal to S, fi? i ; then will Sydx he the dillance of the picture for the inclined plane. Make V x,»2 2, equal V x, dx, and m z will be the meafuring point. The pidlure being thus prepared for delineating the fquare, draw from A, the vifual A ^^ ; and from A, the vifual A, V .r. Draw AX parallel to the vanifliing line t;, SV,a;. Lay on, from A to Wf a fpace equal to the fide of the fquare ; and from w, draw w, m 2, cutting at D. From D, draw a line to i', for the fide I of ( 243 ) of the fqnare D B. Make alfo A N equal to the fide of the fquare ; and draw N m^ cutting at G ; and laftly, draw G V a", cutting at B ; and the fquare will be completed as required. Method fecond. — From A, fweep the arch /^K, whofe radius is equal to the fide of the fquare to be reprefented. Draw A u equal to the angle of the inclined plane with the ground ; and from Zif, draw u t parallel to the ground line ; from t draw a vi- fual to P ; and from u, draw u M, cutting at D ; from A draw a line through the interfedtion of uM with f P, and produce this line till it find the vanifliing point V.r in the perpendicular PV. From D draw a line to v, as before ; and laftly, from G, found as before, draw G V .r, cutting at B, and the fquare will be completed, as in the other method. Obfervations. — If the original plane irfciined to the ground in an angle of forty-five degrees, the vifual line of the fide of the fquare A D would pafs through the diagonal of the fquare A, /^, n, 8, and tend to the upper V, the vanifliing point in that cafe ; and V v would then be the vanifliing line, S would be the center of the picture, m the meafurmg point, and <f 3 its diftance, and v^dSyQ, would be the angle of the inclined jDlane, which is the diagonal of a fquare v,d3^Q,7;2. It is evident then, that the true reprefentation of a fquare in any inclination, wduld H h 2 defcribe C 244 ), defcribe a quadrant of a circle, whofe radius would be the fide of the fquare reprefented, as the figure fliows. N. B. No. I is the fame problem, diverted of all lines but fuch as are abfolutely necefTary to its reprefentation ; which, it is prefumed, will be readily underftood by infpedtion, after what has been faid on Fig. 11. See page 224. Prob. X. Fig. 12. Plate XVIII. To reprefent a Floor of Squares parallel to the FiHiire. G R is the ground line, and H L the horizon. Let s be the center, and d the dillance of the, pidure. Let it now be required to reprefent thirty-lix fquares. Operation. — Lay A D, the fide of the original fquare, fix times on the ground line G R, contained between A i*, as the figure fhows. Draw from each divifion on the ground line vifuals to 5 ; and from h^ draw a line to d^ the diftance ; which line will cut each vifual in i^k^l^p^q^r. Through the feveral ^A^."/7- /"^■■'' ^h/'fs &/yysms. J^/aAf J,9 T Sl<rr-ali,iil)<:l UrM/Zicr/ c^.r t/i,- Acf r/lWr^s [fV t?.T,-rrv. Jjf7/F I'i . 1/^92 ( 245 ) feveral points of interfedilion marked by thefe letters, draw lines parallel to G R, the ground line, and there will be pror duced the number of fquares required. But if it be neceflary to fill up the picture with thefe fquares, and there be no room for laying A D on the ground line beyond >6, then continue the laft parallel line r o a b c the whole extent of the pi6ture ; and take a equal to the fide of the fquare, and repeat it a, b^ c, as may be neceflary. From i, draw s b, produced forward to the ground line. In the fame manner draw s c forward, and fo on re- peatedly. Then, laftly, draw parallel lines from the former fquares, by which means the pidture will be filled up to the fides. Obfervations. — The diagonal line hd pafles through the oppofite angles of the large fquare A, r, a^ b, which includes all the other ; and a line through the oppofite angles of any of the fmall fquares, will alfo tend to the fame point of diftance d. 6/ ( 246 ) ti Of the Reprejentation of Rectangular Solids in different Pofitioni to the Pi&ure. Prob.XI. Fig. 12. Plate XVIII. To reprefent a Row of Cubes ^ or a Prifm^ parallel to the PiHure. Operation. — The ground line, horizon, &c. remaining the fame as for the floor of fquares, draw A, B, C, D, a geome- trical fquare, equal to one fide of the cube. Draw the vifuals A J, B J", C J", D J. From D, draw D o', cutting at i. Draw 1,2, parallel to the ground line, cutting T> s at 2. From 2 raile a perpendicular, cutting C J in 5 ; from i raife a perpendicular to 4, cutting Bj- in 4. Laftly, from 4 draw a line to 5, parallel to the ground line, or to BC; and the reprefentation of the firft cube will be completed. Next, from 2 draw 2^, cutting at 3; draw 3, 8, cutting D j in 8 ; from 8 draw 8^, and it will find the bafe of the fecond cube ; and repeating every thing as in the firft cube, any number of them may be drawn till they vanifli in the point s. Obfervations. — If a number of cubes, or prifms, are to be reprefented in various places on the picture, it will be done with ( 247 ) with the moft eafe, fiift, to reprefent a floor of fquares equal to the fide of the cubes, or bafe of the prifms. Thus, for in- flance, the prifm r is eafily delineated on the back part of the picture, by raifing a perpendicular M N equal to the oi iginal height of the prifm. Draw N J", and from any fquare where it is to ftand, raife perpendiculars cutting Nj at r. From r draw a line parallel to the ground line, which will complete the prifm. In like manner the cube ki may be reprefented any where. Laftly, we may fee, in the reprefentation of a cube, that it confifls of three different cafes of geometrical fquares ; that is, A,D, 1, 2, is the reprefentation of a fquare lying on the ground ; and 1,4,5,2, is the reprefentation of a fquare perpendicular to the ground, and parallel to the picture: and D,C, 5, 2, is a fquare reprefented both perpendicular to the ground and to the pic- ture. The other three fides of the cube are refpedlively parallel to thofe we have mentioned, and therefore are the fame in all refpedls. Prob. ( 248 ) Prob. XII. Fig. 13. Plate XVIII. To reprefent tivo Rozvs of Cubes oblique to the Pi&ure. Operation. — GR is the ground line, and HL the hori- zon. Let s be the center of the pidlure, and s d the diftance. From d^ draw d V, cutting H L in V, and parallel to that fide of the original cube ; whofe reprefentation is A B C g. Draw dv 2X right angles with ^V, cutting at v\ then will v be the vanifhing point of the right hand fide of the fquare. Make VM equal V^, and vm equal vd\ then will M m be the mea- furing points. From A, the angle of the firft cube, draw the vifual A V. Draw alfo A V. Make A B equal to the fide of the cvibe, and from B draw B V, B i;. Next, \3c^ A B to 7, and from 7 draw a line to the meafuring point m^ cutting at a. Lay A B to c ; and from c draw c M, cutting at g ; from g and a raife perpendiculars to C and D ; from D draw a line to V, and from C to V, which will complete the reprefentation of the firft cube. The fpace between the cubes being confidered equal to the fide of the fquare, repeat A 7 each way on the ground line, as often as there is room, as at 8, 9 — d, e,f. From each of thefe divifions ( 849 ,) clivilions draw lines to their refpecStive meafuring points in M, cutting Kv'xwb and in 2, and AV in hik. Raife perpendicvilars from b and 2, cutting the upper vifuals. Do the fame from the other points h i k, and proceed in all refpedls as with the firft cube, and there will be two more produced. . Obfervation^.-— If it. were required to veprefpnt fwo ^di- jtional cubes to each row, it is eyicjent that we mu^ h^ve recoyrfe to fome expedient for this pu.rppfe ; bec^iufe Jhere :i§ not ropnii beyond 9 and /to I9.7 on: any more divifions. Thecefbre from a produce a line parallel to the ground hne, and from /^ do the fame. And obfervie, that a line from 8 to w, and. from e to M, (PUt thefe parallel lines at « and i, ; Ejitend the compafles from i to 2, and repeat this at 5, 4, g, 6^ and from thefe diyifions draw lines to m, and they will cut the vifual Av ia the fame points in which it would have been cut if thefe lines had been drawn from the original divifions on the ground line. Laftly, a line from ^ to M will cut thjn left hand parallel gt/?;; repeat nk zt pqr^ and proceed as before. By this method, which is quite (imple, it is evident we m^y draw as many cubes as we pleafe, by adding parallel lines to the ground line. ii Of ( 250 ) Of drawing Vtjual Lines tending to Vanijhing Points out of the Pi&iire. In the pra(Slice of drawing it is frequently found, by expe- rience, that if we make ufe of a fhort diftance, the figure we reprefent will appear diftorted and unnatural ; and w hen we, to avoid this, make ufe of a long diftance, it will perhaps ex- ceed the paper or picfture we draw on : alfo, in the reprefenta- tion of objedls obliquely fituated to the pidlure, their vanilhing points not being in the center, it often follows, as the confe- quence of choofing a long diftance, that the vanifhing points far exceed the limits of the pidlure. To alleviate thefe difficul- ties, we propofe the following problem. Prob. XIII. Fig. 14. Plate XVIII. 'To reprefent two upright Prifms obliquely Jituated^ whofe Difianee and Vanijhing Points exceed the Limits of the Pi&ure. Let the double line on each fide of Fig. 14 be confidered as the boundaries of the pi^ure. Draw, as ufual, the ground line G R, and the vanifhing line H L, and make s the center of 6 the ( 251 ) the pidlure. Let sdhe confidered as only half the diftance, be- caiife there is no more fpace on the picture above d. From the point d^ draw a right line each way, at a diftance from J-, equal s d, forming a right angle ; becaufe the fides of the prifms are originally perpendicular to each other. Make v m equal v d; then would m be the true meafuring point, provided sd were the whole diftance of the picture ; and in this cafe vv would be the vanifliing points of the fides of the prifms ; but fince sdis only half the real diftance, take in the compafles j- m, and repeat that fpace to M, and make sM^s M, equal, then will M M be the true meafuring points to the whole diftance. Pro- duce the vertical line ds to A, cutting the ground line at A. Divide s d into any number of equal parts, as i, 2, 3, 4, and, for the fake of accuracy, fubdivide thefe as in the figure. Lay on the fame divifions downwards from s to A. The next thing to be confidered, is to draw a line perpen- dicular to the horizon, of fuch a proportion to s d, at any given diftance from j, the center, according to the boundaries of the picture, that when a line is drawn from d, touching the top of the faid perpendicular, it would exa6tly tend to the true vanifliing point, were it produced to the horizontal line. We fliall fuppofe then, that a perpendicvilar line is drawn from the point v, which is exadlly half the diftance from j- the center, to V the vanilhing I i 2 point ( 352 ) point out of the pi£lure. Make then the faid perpendicular line *> 4, half the length of sd\ then a line pafhng from t/ to 4 would, if produced, terminate at V, the true vanifliing point. Divide <y,4 in the fame manner as sd^ iand downwards from <y to ^ lay 6n. the fame divifions ; for v 3 is half the length of s A* Laftly, rnake the other fcale on the left in the fame proportion, then will the picture be properly prepared for delineating the pro- pofed prifms. Operation. — From A draw a linfe to 3, which will be the •vilbal fdf the bottoms i>f the prifms, for A 3 produced would tend to V. Make A c equal to the diftance which the prifm is fuppofed to be from the pidlure ; then, from c, draw a line to Mj Cutting at p ; from /> lay a ruler dctx)fs the two fcale lines, and move the ruler backward and forward till its edge coincide with />, and any correfpondent divifion on each fcale. The ruler being thus fixed, draw a line p b^ cutting tlie fcale line j A in the fecond divifion, an<l the fcale line 1^ 3 to the left in the fame divifion ; then would p b produced terminate in a point on the horizon equally diftant from i as V is. Make A a equal to the left fide of the prifm, and draw a M, cutting at b. Make € e equal A a ; and from c draw a line to M, cutting at h. From the points p^ b, h, raife perpendiculars at pleafure. Confider ( 253 ) Conlider now the height of the prifm, which we fnppofe to be A B; from B place the edge of the ruler, and move it till it be at fimilar divifions on each fcale line, as before. The ruler being in this pofition, draw a line cutting the perpendicular/) D at D ; and from D, place the ruler till it coincide with fimilar divifions on each fcale line on the left, which will complete the reprefentation of the firft prifm ; and for the fecond, proceed in the fame way, obferving that, as there is not room on the ground line G R for repeating the fide of the prifm c e, the fcale line, or new ground line h i k, muft be found, as in the preceding problem, by drawing through b a line parallel to the old ground line, cutting at g^ then muft the fpace h g be laid to / and ^, from which lines being direcfled to M, they will cut at lo. Obfervations. — In Problem XXI. page 71, Plate II. Fig. 15, the geometrical principle is explamed, upon which this method of drawing vifuals to points out of the picture is founded. We there fay, in page 72, *' In whatever proportion the extreme line E P is divided, into the fame proportion will the hypothenufe line EO be divided." Agreeably to which, we may obferve in the perfpe6tive problem before us, that, in whatever proportion the diftance s d is divided, a line being drawn from the faid divifion parallel to the horizon, will cut 5 the ( 254 ) tlie vifual dY in that fame proportion. The Hne s d being di- vided into two equal parts, a hne from 2, parallel to the hori- zon, will cut at 4, which divides the vifual d V into two equal parts ; and a line from the point 4, perpendicular to the hori- zon, will divide s V in the fame manner. Hence it is evident, that a s d^ V 4, be divided into the fame number of equal parts, a line drawn throvigh any two correfpondent divifions, will tend to V, the vanifhing point. It is alfo evident, by the fame mode of reafoning, that if the half diftance s d were prodiiced to twice its prefent length, which woiUd then be the whole diftance, a line from ^ to V would be equal to the fpace from V to M, on the left the true meafuring point, in the fame manner as di) mea- fures V in^ which is only half that fpace. Of reducing the Point of Difiance, fo as to bring it within the Limits of the PiHure. In making defigns on a large fcale, it is very common for the point of diftance to exceed the bounds of the paper or board we draw on : to avoid the inconvenience of which, let the fol- lowing problem be attended to. Prob. C 255 ) PROB.XIV. Fig. 15. Plate XVIII. To find the Reprefentation of a Number of Squares when the Dif- tance is out of the Limits of the Picture. The double lines which include the fquares, are the boun- daries of the paper, board, or picture we draw on. Operation. — Let s be the center, and let sdhe fuppofed half the length of the point of diftance. Make then a fcale on the ground line, whofe equal parts fhall be equal to half the fide of the fquares to be reprefented, as 3, 4, 5. Lay on from 3 to 4 half the fide of the fquare A, and from 4 draw a line to d^ half the diftance, which will cut the vifual 3 J in the fame point as it would have been cut if d had been twice its prefent diftance from J, and the whole fide of the fquare had been laid on the ground line, as at 5 ; for it is evident, that a line from 5 through / would terminate in a point on the horizon twice the diftance of sd. From 4 lay on 5, 6, equal 3, 4, and drawing lines to d, Ave fhall have the fquares B C. Here the learner muft obferve another difficulty arifing ; for the ground line of the picture is filled up at 6, and we are fvippofed to want the reprefentation of three more fquares ; and as the point 6 is near the extremities of ( 256 ) of the pidlure or board we draw on, there can be no opportunity to lay on the fides of the fquare any further; we muft again therefore reduce the length of the point of diftance to />, which is only one fourth of the whole diftance ; in proportion to which we muft alfo reduce the fcale on the ground line to one fourth of the fide of the fquare, as i, 2; or, which is the fame thing, divide the fpace 5, 6, into two equal parts, and from 6, 0, 5 draw lines to h^ and three more fquares will be cut off on the vifual line 3, j, as is evident from the figure. Obfervations. — The truth of the reprefentation of the three laft fquares will appear, if the whole fpace between 3 and 6 be placed from 6 to 9. Draw then from 9 a line to </, which will cut the vifual in the fame points as before, when a line was drawn from 6 to h. The advantage of this problem is very much experienced in the reprefentation of long ranges of buildings, fuch as the in- ternal views of ftreets ; in which cafe it is impoflible to find room on the ground line for the full meafurement of each front, not even when we have a very large board to draw on. I remember to have been very much embanafl^ed myfelf in drawing th^ view of a long ftreet, till I was informed of the above methods.- SECTION ,0^ y "25.pi 2 Pclvocnal ficjiires . noit/a Tllxial,,, M /'Mlj/,J a.r lA^X-/ J-r^/.- A- t:7hr, [u^^il^tft. ( 257 ) SECTION IV. Of the reprefentations of Polygonal and Curvilinear Figures — con- taining fome further Remarks on the Difference between the Re- prefentation of ObjeBs on a Plane^ and their real Appearance to the Eye. — Of long and Jhort Dijlances, and the Reprefentation of <i Row of Columns and PilaJierSy parallel to the Pi&ure ; to- gether with fome Obfervations on the "Theory of Circular Obje&s. Of Polygonal Figures, Lines in three different pofitions to the pi(5lure, will re- prefent any polygon in any lituation whatever *. A pentagon may have one fide parallel to the picSlure ; and if fo, the other four will be oblique to it ; or it may be placed fo as to have all its fides oblique. * See the definition in page 49, and the various kinds of polygons in Plate II. K k A hexagon ( 258 ) A hexagon may be fo placed as to have two fides parallel, and the other four oblique, as Fig. i6, Plate XIX. or it may have all its fides oblique. An odtagon may have two fides parallel to the pi6ture, confequently there will alfo be two perpendicular to it, and the remaining four will be each of them oblique, as Fig. i8, Plate XIX. The odtagon in this fituation, therefore, introduces all the variety of pofitions of lines that can exift in a picture, when the figure is fuppofed to be on the ground plane, or per- pendicular to the picture ; and fince the theory of lines parallel, perpendicular, and oblique to the ground line, &zc. has already been confidered and applied to pra<Stice in the preceding fedtion, in the reprefentation of geometrical fquares and of cubes, no- thing is requifite here, but to apply the fame principles to the reprefentation of polygonal figures. The moft ufeful of thefe are the hexagon and odtagon; which, for brevity's fake, I fhall confine myfelf to, taking, it for granted that, after the learner is acquainted with thefe, he will be able to delineate any othei, from a pentagon to a duo- decagon, as it may be found requifite. Prob. ( 259 ) Prob. XV. Fig. i6. Plate XIX. To reprefent a Hexagon having Two of its Sides parallel to the PiBure. Operation. — Draw the ground line and horizon, and make J- the center of the pi6ture, and d the diftance. Throvigh d, draw a line at pleafure parallel to the horizon. From d defcribe a fe- micircle, in which may be infcribed half a hexagon, as i, 2, 3. From £/, through each angle of the hexagon, produce a line till it cut the horizontal line in V "y ; then will V i; be the vanifliing points of the four fides of the hexagon, which are oblique to the piaure. Draw the vifuals F <y, B "u, and B V, F V, and make B D and FA each equal F B, the fide of the given hexagon. Draw A V, cutting the vifuals at i K ; and draw^ D i\ cutting at O N. Laftly, draw K N parallel to F B, and the reprefentation will be completed as required. Obfervations.— It is evident that a hexagon is compofed of fix equilateral triangles. The reprefentation contains fix tri- angles alfo ; and if a right line be drawn through each oppofite angle, as from F N, &c. they will all interfedt in the center ^, in the fame manner as the lines from each oppofite angle on the K k 2 plan ( 260 ) plan of the hexagon Y interfe6l each other in the true center, from which a circle may be defcribed that will touch each angle. Prob. XVI. Fig. 17. Plate XIX. To find the Reprefentation of a hexangular Prifm^ or Box, having two Sides parallel to the Figure, as before. This problem may be folved by another method, which will help to confirm the truth of the laft method. Operation. — Draw the plan Y, and produce its fides up to the ground line at g,f b, c. Find the vanifliing points v V as in the preceding problem. Draw the vifuals g^^f V, and bv, cv, which will interfecSt each other at a, e, t. Through e the cen- ter, correfponding with e- on the plan, draw h u parallel to -7, r, on the plan. From v, draw v h, produced to ; and from V, draw V z/, produced to n. Laftly, from n draw ;z 0, which will complete the bottom of the box. Or it may be done by drawing the vifuals 8 V, 7 V, when the other vifuals are drawn, as the figure itfelf fufficiently indicates. From each angle of the bottom perpendiculars muft be raifed, and produced at pleafure. Next, draw gp perpendicular to the ground line, and make ( 26i ) make gp equal to the height of the box ; and draw p V, and produce n, o to /; and from / draw i k^ and from k draw a line parallel to the ground line, which will cut the aforefaid per- pendiculars drawn from o, ;z, at i, 6. The perpendiculars from h, a, were cut by /> V at 2, 3. Draw 6 V, and i V, cutting the perpendiculars from u and / at 5, 4 ; from 5 draw 5 v^ and from 4 draw 4, 3, and the outlines of the box will then be com- pleted. To fliew the infide, and the thicknefs of the edges of the box, proceed thus : — produce from the plan, x w, and from iv draw a line to V, cutting / ; from its interfedtion in / 0, raife a perpendicular to /■ i ; and from its fedtion on k i, draw a line to V ; and where this line cuts the diagonal 2, 5, a line muft be drawn from v, the vanifliing point, to 9, the point of inter- fetftion, and produced till it cut the diagonal i, 4, at i ; and from where it cuts this diagonal, draw a parallel to 1,6; and from where it cuts at 6, draw a line to V ; and from where this line cuts at 5, draw a line to ^', cutting 4; and from where it cuts at 4, draw a line to the other interfedtion at 3, and the edges of each angle will be finiflied. Obfervations. — ^The hexagon in this figure is nearly the fame in its plan as the other in Fig. 16 ; but as it is removed back from the pidlure, its appearance is more eafy and natural than ( 262 ) than that. The hexagon in Fig. i6 has one fide, F B, in the pidlure, therefore F B is the full length of the fide of the ori- ginal hexagon, and the contradtions of the other fides appear more fudden, and therefore more unnatural ; but its repre- fentation is equally true. The hexagon may, however, be re- prefented by this method as far back as we pleafe, by repeated- ly laying F B, the fide of the hexagon, on the ground line, as from D to E, and drawing E v, by which means we have another hexagon i, 2, 3, 4, K, Z, whofe appearance is perfedtly natural. PROB. XVII. Fig. 18. Plate XIX. To Jind the Reprejentation of an Ociagon, having two Sides parallel to the Pi&ure. Operation. — Draw GR, the ground line, and HL as in common ; and make j" d the diftance of the pidlure, and s the center. Draw half the plan of the odlagon at A, as follows. — Make b g equal to half the breadth of the plan ; and from c fweep the arch b^ /, e. Bife£t the arch in /. From / draw / c, cutting at p^ and^^ will be half the fide of the o6lagon. Lay on bp to b I, and a line from /> to i is one fide of the odagon. 7 Produce ( 263 ) Produce each fide of the 0(5tagoii up to the ground line ; and from the points/, 8, i, b^ draw vifuals to j". From 8 draw a hne to 4 cutting at 7 ; from i draw a hne to d alfo, cutting at 6. From 7 and 6 draw hues parallel to the ground line, cutting at 2, 3. Draw fdy paffing through the diagonal of the fquare in which the odtagon is infcribed. Draw 4, 5, parallel to the ground line. Laftly, draw the fides i, 2, — 3, 4 — 4, 5 — 5, 6, and 7, 8 ; which completes the reprefentation. Prob. XVIII. Fig. 19, Plate XIX. To find the Reprefentation of an o&angular Prifm^ or BoXy having all its Sides oblique to the Picture. Operation. — Draw the ground line and horizon, and let figure A be half the plan of the odlagon. Let s be the center, and d the diftance of the pi<Sture. Produce n e, n p^ to the ground line ; and draw g perpendicular to e. From b, g, i, R, draw vifuals to s ; and from R draw R d; by which a fquare will be reprefented in which the odtagon may be infcribed. Draw the other diagonal of the fquare, which will cut the vifual g J- in 8 ; the other diagonal R dy cuts the vifual g s in 6. From ( 264 ) From 6 draw a parallel to 4, cutting the diagonal at 4; and from 8 draw a parallel to 2, cutting the diagonal at 2 ; through the center of the fquare draw a parallel, cutting at 7 and 3. Laftly, draw right lines to each point, and the bottom of the box will be completed. Draw A F parallel to G R, and at a diftance from G R equal to the height of the box. Then reprefent another fquare A, F, G, D, and draw the diagonal each way. Then from 8 raife a perpendicular to 10, cutting the diagonal A D at 10. In the fame manner, and to the fame effecft, raife a perpendicular from 6 to 11, from 5 to 13, from 4 to 14, from 3 to 15, from 2 to 16, from i to 0, and laftly, from 7 to 12. Draw then, as before, right lines to each point, and the whole reprefentation of the box will be finiflied, except fliewing the infide and the edges of the box : having defcribed how this is to be done in Problem XVI, I need not here repeat it ; only it will be neceftary to obferve, that as the fides of the oilagon are drawn by this method without vanifliing points, thefe points muft be found by producing the fides of the odtagon till they cvTt the horizontal line H L, in the fame way as the fide 15, 14, is produced to v, which will be the vanifhing point required for drawing the infide line to, as the figure fliews. Some ( ^65 ) Some further Remarks on the Difference between the Reprefenta- tion of ObjeBs on a Plane^ and their Appearance to the Eye, We have already, in page 210, obferved, that a perfedl pi(Slure of objedls, as they appear to the eye, cannot be deline- ated on a plane ; we may conceive it to be done on the furface of a fphere, if the fpedator's eye be in its center. But this is only a fuppofition ; for, in reality, there can be no ftri^l rules given for drawing perfpedlive lines on a fpherical furface. A painter, in delineating objedls on the infide of a large dome, may make ufe of flraight lines, and the rules of perfpe6live, as applied to a plane ; but he does this, becaufe he perceives that the dome being exceedingly large, and the objedt but fmall, the fpace which the faid objedt occupies on the dome is nearly a level furface; and therefore common perfpe6live comes near enough to the truth for drawing that fingle object. But if the objed: be large, and the dome fmall, nothing of this fort can be applied. Mr. Kirby has, indeed, propofed a method to draw per- fpedive reprefentations upon vaulted roofs and domes ; and, for L 1 any ( 266 ) any thing I know, it is as good a method as can be adopted ; yet it cannot be called perfedt, much lefs a fyftem of linear per- fpe<5tive applicable to fpherical furfaces *. But the ordinary rules of perfpedlive applied to a plane is a perfedt fyftem, as it relates to the reprefentation of objecSts ac- cording to their real appearance on a tranfparent plane inter- pofed between the eye and the original figure of any thing : for the tranfparent plane, in this cafe, is a feflion of the rays of light coming from the obje£l to the eye ; which fe<5tion is there- fore an infallible and moft perfe6l perfpecftive reprefentation of the original figure on a plane ; but it is not fo perfecSt to the eye, becaufe the eye is globular. Perfpedlive then, as it refpe<5ts the appearance of objefts on a plane, is perfe<St, and its rules are ftridlly mathematical ; but as it refpe<5ls the appearance of thofe objedts to the eye, it is a deception, and is therefore liable to defedts and imperfections, as every other deceptive art is, owing to various circumftances de- pending on the management of the artift. Thefe diftindtions have not been fufficiently attended to by fome, which has therefore been the occafion of fome difputes on this fubjedt not well founded. * As this fubjedt is foreign to my purpofe, and not likely to be of ufe to thofe perfons 1 wi(h to ferve in this work, 1 ftiall not enter upon it ; but if the reader choofe, he may confult the third fedlion, page 74, of the above gentleman's book. 8 Hence ( 267 ) Hence it has been faid, by a certain writer, that a row of cohimns, or cylinders, cannot be reprefented parallel to the pi<5ture, without producing a clumfy and bad effedt, if they be drawn according to the flri6t rules of perfpedtive ; for then thofe columns which are furtheft from the center will be the largeft, which ought rather to be the fmalleft, according to their appearance to the eye. But this depends on circumftances, and is not a fufficient reafon for charging the rules of perfpedlive with fallity, or even a defeat, unlefs the laws of this art ob- liged us always to choofe a very fliort diftance ; and that, when we view a picture, we muft ncceflarily hold our nofe clofe to it, before we can be a judge of the merit of perfpedlive. From pretty much the fame principles another gentleman, who writes on this fubje(5l, gives us an inftance of the imper- feftions of perfpedlive, by reprefenting a geometrical fquare, with a very fliort diftance, which occafions the fquare to look too long one way, which he therefore terms a falfe reprefenta- tion, though he has obferved the ftridt rules of perfpedtive. Yet I will venture to fay, having made the experiment, that if this gentleman had placed his eye perpendicular to the center of the pidlure, and at a diftance from it equal to that by which he drew the fquare, he would not have difcerned any bad effe£t even in that which he calls a falfe reprefentation. But that the learner may have a proper view of this fubje(a, I fliall firft re- L 1 2 prefent ( 268 ) prefent a row of columns as they appear to the eye ; ancl, fecond- ly, reprefent the fame row as they appear on a plane, by which the learner will fee the difference between Mr. Kirby and Mr. Mal- ton's opinions on the fubjed;. And, thirdly, w^e fliall lliow the aforefaid row of columns on a plane, having the advantage of a long diftance, which, in this cafe, is recommended both by Malton and Noble ; the eifeil of which being a proof that we may abide by the ftridl rules of perfpe<5live in delineating a row of columns, or any other cylindrical objedt, and that more pleafant to the eye than when they are reprefented according to Mr. Kirby's opinion and definition of perfpecStive, which is, " to draw the reprefentations of objects as they appear to the eye." See page 94 of his Treatife on Perfpedlive. Firft, to dehneate a row of columns according to Mr. Kirby's definition. Of the Reprefent at ion of a Range of equidiflant Columns parallel to the Pi&ure. First, Let I, K, L, M, Plate XX. Fig. 20, be confidered as a horizontal fedtion of the four columns A, B, C, D ; and let the arch 1,2,3,4, ^c. be the fedion of a fpherical picflure, and d the diltance of the eye from the pidure, then will s be its cen- ter. jL(/mr/ist/ifi / Co litmus J'l^t^.2<:>. r.'y,r^„y-, //,-/ S^U-^/^f^. /itfi/t/?t^^/ >z.''r/,'Ac( .Jtfff.t ^>- <^.7lfry- . J?e<'''2if ^^^2 . ( 269 ) ter. Draw from the apparent diameters of each column vif\ial lines to d\ and where thefe rays cut the arch at i, 2, 3, 4, &c. will be the reprefentation of the diameters of the four columns as they appear to the eye. Thefe diameters and their inter- columns, or fpaces between, muft now be transferred to a level plane or picture, as in No. i. Draw a hne AB, and take 1,2, from Fig. 20, and place it at i, 2, No. 1 ; then take 2, 3 from Fig. 20, and place it to 2, 3, No. i, and fo of all the others. Draw perpendiculars from each number, and flnifli them, as exhibited in the figure, and they will be the reprefentations of the four columns A, B, C, D, as they appear to the eye. Secondly, We fliall now reprefent the fame columns as they appear on a plane, having the fame center and diftance as before. Draw the line PP, Fig. 20, parallel to the four columns, which will be the fedtion of the picture ; and fince the vifual rays from each column were drawn before, the reprefentations of the apparent diameters of the faid columns on a plane will be at ab^c e,fg, h i. Transfer thefe diameters and their inter- columns to No. 2, as the figure fhews ; then will A, B, C, D, be the appearance of the four original columns at Fig. 20, on the plane of the pi(Slure, according to the ftrid; rules of per- Ijpedlive.. Now ( 270 ) Now the queflion is, Which of thefe reprefentations are moft alike to the originals in Fig. 20 ? If the reader will place his eye perpendicular over A, the center column in each repre- fentation, and look through his hand at a diftance equal dSy Fig. 20, 1 believe he will be able to determine for himfelf ; never- thelefs it may be proper to offer fome remarks by way of aflift- ing his inquiries. And, firft. We may obferve that the whole fpace which includes the columns at No. 2, is confiderably nearer the length of the ori- ginals at Fig. 20, than the fpace which No. i includes. The intercolumns are nearer alike at No. 2 than they are at No. i. And, laftly, if we look fteadily through our hand as above di- rected, we fliall find that, at No. 2, the apparent thicknefs of the column D will be greatly reduced, and that of C will be alfo reduced, and both in proportion to their diftance from the center, fo that there will not be much difference in the thicknefs of each. But if we look in the fame manner at No. i, we fhall find the reprefentation appear worfe, for D C will appear fmaller than they are reprefented. The reafon is obvious, for the rays of light by which vifion is performed, being confiderably ob- lique at the column D and C, the optic angles which they fub- tend are much lefs than thofe fubtended by A and B, as Fig. 20 clearly demonftrates; for the rays G d^Hd^ are more oblique to the ( ^71 ) the pidure PP than the rays N«', Od; therefore we fee that the arch 7, 8 is lefs than the arch 5, 6, and fo of the reft in pro- portion. The figure alfo demonftrates, that when thefe vifual rays are cut by a plane P P, parallel to the original columns, the ef- fecSl is reverfed ; for then the reprefentative diameters will in- creafe as they decline from the center j, yet the optic angles under which they are feen remain the fame as before, when the vifual rays were cut by a fpherical pi<Slure at i, 2 — 3,4, &c. Hence it is evident, that the diameter d /, viewed by an eye at d, would not appear larger than the diameter 7, 8 on the arch» Wherefore the true reprefentations of the original range of co- lumns as they would appear on a tranfparent plane, interpofed between the fpe6tator's eye and the faid original columns, are at No. 2, not at No. i, for that is their reprefentation on a fphere, as they appear to the eye, anfwering to Mr. Kirby's definition of perfpedtive, though this is not what he means to recommend in practice ; for he fays, page 97, " that they" (meaning a range of cquidiftant columns) " fhould be fo reprefented as not to offend " the eye of a common obferver ;" by which he means they fhould be drawn of one thicknefs, and at equal diftances. How far the reprefentation at No. i, which is according to his defini- tion. ( 272 ) tion, will agree to this, I will leave to the judgment of the reader, and fhall proceed to Ihew how thefe columns may be reprefented, according to the ftridl; rules of perfpedtive, fo as to appear of one thicknefs, and at equal diftances. We have hitherto fuppofed the eye of the fpedator at ^, viewing the original columns A, B, C, D, Fig. 20, in which fitu- ation the vifual ray H dy from the fartheft column D, and the eye's axis d j, form an angle of fifty-four degrees ; and fince s i is but half the pidture, the whole would be feen under an angle of one hundred and eight degrees, which is far too great for viewing any picture ; for the eye at d cannot take in a fpace twice the length of j- /, without being ftrained and twifted. To convince the learner of the truth of this, let him take a pair of compafles and extend them from d to j, and placing one foot on the column A, at No. 2, let the other foot keep his right eye from A, exa6tly at the diftance of their opening, equal ds. Obferve, the compafs foot muft nearly touch the right eye, or the experiment will not be fo ftriking. The eye beiflg thus placed, experience will teach him that he cannot fee the column D at No. 1 without twilling his eye ; and at the fame time he will fee, as we faid before, that the columns will be nearly equal in thicknefs. But if the eye d, at Fig. 22, be removed back to E, the ( 273 ) the whole pi6lure will be feen with eafe, for it will only fub- tend an angle of forty-eight degrees ; and at this diftance, the vifual rays being not fo oblique to the picture as before, they will cut it nearly at equal diftances from each other, as is de- noted by the afterifms ■'•■ *, where the dotted rays cut PP. The good effedl produced on the pidure P P, by choofing E for the diftance, is clearly demonftrated by Fig. 21, which exhibits the fame row of columns drawn by the diftance E. Thus: — Mak.es d, Fig. 21, half the fpace of Ex, Fig. 20; becaufe there is not room for the whole diftance on the plate. From s draw sA perpendicular to H L. Draw GR as a groimd line, and proceed as before to lay on the fpaces marked by the afterifms * *, Fig. 20, on the line P P. Draw then the vifuals from A, B, D, C, as the figure Ihews. From i, Fig. 23, draw a line to 4 cutting A j- in 2. Through 2 draw a line parallel to G R, cutting the vifuals ; by which will be reprefented four geometrical fquares, in which the bafes of each column will be infcribed. Laftly, from the circles contained in each fquare, draw the fliafts, and finifli them as in the figure. Now let the reader place his eye per- pendicular over s, and at a diftance from s equal twice sd; then 1 am perfuaded he will fay, that a common obferver would pronounce the columns of equal thicknefs, and their inter- columns cquidiftant, although they are reprefented according M m to ( 274 ) to the Ih i(ftcft rules of perfpe<flive ; which Mr. Kirby thinks we miirt not abitle by in this cafe. Before I conchide this head, it may be proper to take fome notice of the reprefentation of a row of equidiftant pi- lallcrs. A little reflection will make it evident, that the reprefenta- tion of a row of pilafters parallel to the picture, are not fubjed: to thofe awkward appearances which columns are, owing to a Ihort diftance. For, Let the dark line 9, 10, on the column D, Fig. 20, be a pi- lafter, equal in width to 13, 14, on the column A. Draw the vifuals 9, 10, to^, cutting the picture PP at 11, 12; then will the fpace 11, 12 be equal a b, cut by the rays from the pilafter 13, 14; for as the pilafter 9, 10 is to 13, 14, fo will 11, 12, ^Z*, their reprefentations, be to each other. The fame reafoning fliows us why columns increafe in thicknefs as they decline from the center of the pidture, if we obferve where the vifual rays, drawn from their apparent diameters, cut the line pafling through their centers, as tv, kl\ wherefore, as /^/ is to 13, 14, fo is h i, the reprefentation of the column D, to a d, the repre- fentation of A. And hence it is evident, that in the reprefenta- tions of buildings whofe fronts are parallel to the pidure, their doors ( 275 ) do^rs and windows will be to each other as their originals are ; that is, if the windows and fpaces between them be equal in width, their reprefentations will be equal alfo ; and, as Mr. Martin obferves, " all plane furfaces whatever, placed in a front wall or plane, will have in their perfpedlives no change of figure at all ; a fquare, a parallelogram, a triangle, a pentagon, a circle, an elliplis. Sec. will be all the fame figures on the per- fpe(5tive plane, and perfeftly fimilar to the originals ; and this will hold good in every part of fuch a plane in front, as well above and below the horizon, as on each fide the eye •^'." Of the proper Choice of the Diflance of the Pi&ure^ proportioned to the Height of the Horizon^ and the Nature of the Obje& to he reprefented. From what has now been hinted refpecSling long and Ihort diftances, the learner will naturally wifh to know fome fixed principle about it, and what is the general rule for choofing a diftance. To give him all the fatis faction I can on this fubjed, I fliall propofe the following remarks. * See his Principles of the Genuine Theory of Peifpeilivc, page 51. M m 2 There ( 276 ) There is a certain diflance fliorter than which the eye can- not eafily fee a pidlure ; and therefore if an objeA be delineated by fuch a diftance, it will appear unnatural. In Plate XIV. Fig. i, let B D be the length of the pidture, and Z the place of the fpeflator's eye, and e the center of the pidture, then will Z <? be the diftance of the pidture ; but as Z <? is very little more than half the length of the pidture B D, therefore the angle under which the whole pidture would be feen at Z, is almoft ninety degrees. This is an angle which the eye cannot eafily take in, be- caufc the ray Z B is in a ftate too diverging to the pupil of the eye, and therefore the fpedtator muft twift and ftrain his eye, before he could fee the whole extent B D. The optical reafon of this is as folio w^s ; Produce the vifual rays LP, KP. Now, it is evident, from the fcale on the arch, that thefe rays fubtend an angle of more than ninety degrees. Therefore fince, according to optical laws, rays will not unite in a point on the retina at a greater obliquity than an angle of forty-five degrees, confequently the points K L will not appear to the eye. This is probable enough from the figure ( 277 ) figure of the eye, for the image s of K, and o of L, are too far for- ward in the eye to be feen ; but by turning the eyes a Httle to- wards K or L, it is evident they will become vifible ; for then P^, the axis of the eye, will perhaps be turned to 20 ; or, on the other hand, at 40 ; confequently the angle of obliquity 20, P K, being confiderably lefs than forty-five degrees, the pencil of rays from the point K will unite in a point on the retina, and fo be- come vifible. A fimple experiment will convince the reader of the truth of this. Take a lath two feet long, and at the center fix a wire in a perpendicular direction, about thirteen inches long, or we fliall fay twelve inches, for then a thread ftretched from the wire to each end of the lath would form an angle of 90 ; that is/ the threads will be perpendicular to each other. The end of the wire being held clofe to the eye, the experimenter mull look along each thread at once, and try if he can fee them diftindtly at each end of the lath at the fame glance, without flraining his eyes. If he continue to do fo a few minutes, the pain which this gives will be a fufficient proof that the eye cannot ealily take in an angle of 90 ; and that therefore twelve or thirteen inches is far too fhort a diftance for a pidure two feet long. Therefore, ( 278 ) Therefore, in Fig. i, if the eye be removed to P, the angle which tlie rays DP, BP make with the picture BD is confiderably lefs, and hence the eye at P will more eafily take in D B, the whole extent of the pidture ; becaufe the rays D P, B P do not diverge fo much at the pupil as before. If, therefore, the aforefaid wire be lengthened in the proportion of P <? to B D, which will be as twenty-one inches are to twenty- four, the whole length of the lath ; and if threads be fixed as before, reprefenting the vifual rays D P, B P, the eye P, placed at the end of the wire, will eafily fee at one glance both the threads BD. This experiment, therefore, induces me to conclude that a pidure which is filled the whole length with obje(Sls on the front, fliould never be drawn by a diftance fliorter than the perpendicular of an equilateral triangle, whofe fides are equal to the whole length of the pidlure. The angle B, P, D, is equi- lateral, and P ^ is its perpendicular ; and that I take to be the fliorteft diftance that fliould be ufed in this cafe. And I will venture to affirm, from experience, that any perfon who has never once thought on this fubje6t, when viewing a picture two feet long, will not ftand lefs than twenty-one inches from it when he wants to fee the efFec5l of the whole ; but if he would examine minutely fome particular part feparately, he will na- 8 tvu'ally ( 279 ) rurally approach nearer to the picture, in proportion to the iize of the part thus examined. Whence, I alfo conclude, if nature is to be a guide in matters of delineation and painting, that the diftance of the pi(5ture fliould be as 21 is to 24, fo is the proper diftance to the fpace which the front objects occupy on the pi6ture. For, fuppofing a pidture two feet long to have only two or three regular objects on the front, occupying not more than two thirds of the whole length, which is lixteen inches, it would not be neceiTary in this cafe to make the diftance twenty-one inches. A diftance of fourteen or fifteen inches would then be fufficient, and produce a more agreeable efFe<fl in the appearance of the regular objecSts, both in front and back, than when drawn by a much longer diflance. For, if front objedts are too much fore-fhortened by a long diftance, thofe on the back ground will be much more fo, and appear too tall for their thicknefs ; and the whole pidture will want depth, efpecially if it be an internal view of a ftreet, a long room, or any thing of this nature, where the eye is fuppofed to be pretty near the firft objedt. I fhall now apply the foregoing principles to a few pradlical cafes, by which the learner will fee the efFedl of long and fhort diftances, and how to choofe them on particular occafions. How ( 280 ) How to choofe a D'l/lance, when the whole Length of the Figure is filled with Obje&s on the Front. Let /) r, o t^ Fig. 22, Plate XX. be the lines which mark out the length of the pidlure filled with fquares on the front. Extend the compaffes from ^; to ^; on the horizon, and fweep the arch i; D, D -y ; then will their interfeftion D be the proper diilance in this cafe, and s will be the center. Make s V each way equal s D, and V will be the working diftance, as the figure fliows. The fquares C, K, N, O, drawn by the diftance s V, are per- fedlly natural. But the fquares E,P,Q,R, drawn by Ji;, are not fo ; becaufe the diftance is vaftly too fliort ; for the eye at d views the pidlure in an angle of ninety degrees, which, as we have already fliewn, is far too great, and therefore the repre- fentation of the fquares are unnatural to a common obferver. But if the reader place his eye perpendicular to j, and at a dif- tance from s equal s d, he will find that the unnatural length of the fquares, from front to back, will be greatly diminiflied in appearance. On ( 28l ) On the other hand, it is equally neceffary to avoid choofmg a diftance too long ; the efFedt of which is feen at the fquares F, where they appear too narrow from front to back ; for the dif- tance at z forms, with the whole length of the pidture, an angle only of 48 degrees ; which fliould not be admitted, except in particular cafes, as in the reprefentation of a row of columns parallel to the pi<5lure in Fig. 20, where the eye at E is in the fame angle with the pi6lure twice PP, as at z^ Fig. 22. How to choofe a DiJIance^ when the Qbje&s are drawn by a large Scale^ fituated not far from the Center of the Pi&ure. Let P /, Fig. 22, ftill be confidered the whole length of the pi(5lure ; and let M be the reprefentation of a fquare, on a much larger fcale than that at C ; and let its fituation at M be much nearer to F, the center fquare. From j", the center, extend the compaffes to ^, the extreme point of the pi6ture, and fweep the arch /, c, b^ then will c or ^ be a proper diftance in a cafe of this kind ; for the fqnare M, drawn by the diftance c, appears perfedlly natural, which would be too long were it drawn by V, the former diftance, as appears by the diagonal drawn from 10 to V, cut- ting the vifual 9, s at a. This by no means contradidts what has been advanced in page 178 ; where we fay, that " a picture filled with obje«5ts on the front, fhould never be drawn by a N n diftance ( 282 ) cUftance fliorter than the perpendicular of an equilateral tri- angle, whofe fides are equal to the whole length of the piflure.'* For, let the line 9 be now confidered the bounds of the picture and it will be evident, by drawing a line from b to ^, that the diftance s b'vi, greater to the pi(5lure at 9, than j D is to the pic- ture at /, other wife b g would be parallel to D v. Another advantage may be obferved in this method, if we confider that a very high horizon will produce as much dif- tortion in a pi6lure as too lliort a diftance. Therefore if we fuppofe the horizon to be made higher by the fpace / /, the dif- tance will then be s /, in the fame proportion to it as j c is to s t. r How to choofe a Di/lance, when a Piece of Furniture, not very long, is reprefented by itfelf on the Center of the Front of the FiBure. If a fingle objed:, or piece of furniture, be reprefented by itfelf on the center of the ground line, an equilateral triangle being drawn, whofe fides are equal to the length of the piece of furniture, the perpendicular of this triangle added to the height of the horizon, will be a very agreeable diftance in fuch a cafe. Thus, at the fquare F, fuppofed to be the plan of a piece of furniture reprefented on the center of the ground line, extend the compafles from 10 to at, and fweep the arches, to form an equilateral ( 283 ) equilateral triangle, whofe perpendicular will be at w; then will s w be the diftance propofed in this cafe. Ikit if the piece of furniture be of an extraordinary length in front, in propor- tion to its breadth from back to front, then it will be beft to adopt the preceding method ; for if we fuppofe the piece of furniture to extend from 7 to 9, then a perpendicular of an equilateral triangle of that dimenfion added to the whole height of the horizon, would forefhorten too much. Of thefe things I am perfuaded the reader will be convinced, if he make the ex- periment as the cafes are here ftated. Of the Reprefentations of circular and curvilinear Figures^ both plain and folid\ together with fome Remarks on their Theory. The manner in which fome painters and defigners treat circular objects, would lead one to fuppofe that there is no cer- tain theory on which to build the pradlice of drawing objedls of that kind. Sometimes we may fee a calk, if not fliewing both ends, yet the end on which it ftands is reprefented by a curve confider- ably more flat than that by which its top is fhewn; than which nothing can be more abfurd, for the very reverfe is the truth. N n 2 We ( 284 ) We may alfo fee, in fome cabinet defigns, the bottom of a round fronted chefl of drawers, or commode, reprefented by the fame curve as that which reprefents the top part ; which, though not fo ridiculous as the above, is far from being fcientific or according to the rules of perfpeilive. That the learner may avoid thefe miftak.es, and have a proper conception of this mat- ter, we fliall propofe the following fhort theory. Cafe I. — If an original circle be fituated in a plane parallel to the pi(5ture, its reprefentation will be a circle. Thus : — Let A, B, O, D, Plate XIX. Fig. 20, be an original plane parallel to the pidlure H, I, K, in which is fituated a circle a, b^ d^ e, whofe reprefentation on that pidture is required. The vifual rays from each diameter of the original circle tending to the eye E, are cut by the pidlure or plane of projec- tion H, I, K, in a parallel direcSlion to the original plane A, B, O, D. Wherefore we have the diameter 4, 2 drawn perpendi- cular to a d, its original. Alfo we have the diameter i, 3 parallel- to its original d e; confequently the diameters i, 3 — 4, 2, are the reprefentations of their originals ad^b e. C is the center of the: original circle, and a line from C to E bifedls the triangle b^ E, e% confequently c is the reprefentation of the center C. Laftly, the radii or femidiameters c i, c 2, c 3, c 4, are equal and limilar to their originals, ( 285 ) originals, and therefore any one of them, as c i, will defcribe the circle i, 2, 3, 4, which will be the true reprefentation required. The truth of this may alfo be proved, by conlidering the vi- fual rays 6 E, d E, 8cc. as the fides of a cone whofe vertex is at the eye E, and whofe bafe is the original circle a, b^ d^ e, and its axis C c. Now it is evident, that if a cone have a fe(5lion parallel to its bafe, the curved boundary of that fe6lion is a circle, in like manner as a pyramid, whofe bafe is a geometrical fquare,. produces a geometrical fquare, if its fedlion be parallel to its bafe. See page 230. Plate XV. Fig. 6v By the above theory we fliall eafily judge how to proceed in the reprefentation of arches, when they reft on pillars or piers parallel to the pidlure. And it fliould be obferved, that in whatever fituation the original arch or circle may be in with refped: to the center of the picture, if they be parallel to the pidlure, their reprefentations will be limilar to their ori- ginals -'•■. Cafe 2. — If an original circle be lituated in a plane not pa- rallel to the pidure; that is, if it be the reprefentation of a cir- cular obje<5l lying on the ground, or in any plane parallel * The reader may, if he pleafe, confult Dr. Brook Taylor's fecond corollary of theorem foutih, p. i6» 1 with ( 286 ) with it, its reprei'entation on the picture will be an ellipfis. The reader who has previoufly made this fuhje(5t his ftudy, may afk what I mean by the term ellipfis in this place ? fince fome have difputed whether the reprefentation of a circle in the above cafe be a regular ellipfis, or a curve of fome other fpecies of the conic fedlions. Mr. Noble has difcuffed this point in oppofition to the Critical Reviewers, who had cenfured Mr. Ware in his tranflation of Sirigatti's perfpedlive, becaufe the tranflator had defined the reprefentation of an original circle fituated in a plane not pa- rallel to the pidlure, to be a regular ellipfis. hi oppofition to which definition of Mr. Ware's, the Critical Reviewers for July 1756, page 509, make the following obfervations. " In regard to his regular ellipfis for the reprefentation of a circle, it appears, from the very nature of perfpe6live, that the fore part of a circle will appear more round than the back part, which being further removed from the eye, cannot appear to have the fame degree of curvature ; and confequently the whole figure, if drawn, mufl: be very far from having the form of fuch an ellipfis as is to be made by a tranfverfe and conjugate diameter." Mr. Noble, in oppofition to the above remarks, attempts to prove that the reprefentation in queftion muft be a regular el- lipfis ; but his arguments are fo abHrufe, that if they were founded ( 287 ) founded in truth they would not be convincing to the ordinary reader, and therefore I fliall not trouble him with them, but proceed to offer a remark or two in confirmation of thofe made by the Reviewers, which I think eafily underftood. Let A, B, C, D, Plate XXI. Fig. 23, be the reprefentation of a geometrical fquare in which an o6tagon and circle may be infcribed. The circle, truly reprefented, will touch every fide of both the fquare and oaagon, as fliewn by the figure. Now, I cannot fee by what mode of reafoning we can prove that the ellipfis is regular any more than we can prove that the ocflagon is re- gular, becaufe it is the reprefentation of one that is fo; but, perhaps, to ufe Mr. Noble's words, " we are ignorant of thofe few geometrical praecognitae which alone can render us ca- pable of convidlion on this point :" and this may be the rea- fon why I have confidered Mr. Noble's arguments fo ab- ftrufe ■•••'-. At the fame time I do not think the Reviewers were ignorant of thofe few firft principles of geometry, nor even wanted their recolIe6lion, when they animadverted on Mr. Ware. They jultly fay, " that the fore part of a circle will appear more round than the back part," which muft be evident to every one, by obferving that the whole curve on this fide of the diameter g c, is what they mean by the fore part of the circle, * The reader, if he choofc, may fee the arguments in Noble's Linear Pcrfjiecflive, page 14a, . .'>Ii' . and; ( 288 ) and all beyond ^ c is confi Jered the back part of it. We may alfo obferve, that the curves contained in the quarter parts of the elliplis are not one of them fimilar to another. How then can we pronounce it a regvilar elHpfis ? When we fpeak of the per- fpedtive appearan-^e of any original obje(ft, do we not denomi- nate it by the figure which it alTumes upon a plane, and not as it appears to the eye? where then is the good fenfe or propriety of calling that a regular ellipfis which is no way regular? One would think Mr. Nobfe had forgotten the dif- tincftion which he fo properly maintains in other parts of his book, namely, between the appearance of objedts to the eye, and their reprefentation on a plane ; for if we ftand at a diftance from the top of a round table, it will appear to the eye a re- gular ellipfis ; but if the top be reprefented on a pidture accord- ing to that diftance, it will be an irregular ellipfis, and its irre- gularity will be in proportion to the fliortnefs of the diftance of the pidture. But fuppofe we were to confider b d the tranfverfe diameter, and confequently b f the conjugate, yet there is a manifeft difference between the two femi-ellipfes. Nor is it poflTible to draw a tranfverfe diameter in fuch a direcflion, as that, when the two femi-ellipfes are turned down on each other, they would coincide. Yet it muft be obferved, that if the re- prefentation were drawn in the center, and by a long diftance, it would, in this cafe, approach fo near a regular ellipfis as the difference could not be eafily difcerned. From y-i.ij^i 3 Circu/a.r ci: fur viJif tear I^inunw /■/ -^1 "trry Se Rif/iAl/ as l/lrAct dirtrlr fy <7. Tcfr^.^^lm 4//'</i ( 289 ) From what has heen faid, the learner muft obferve then, that when he proceeds to draw the reprefentation of an original circle, he muft not think of applying the compaffes or trammel to draw it by; but a number of points muft be found, through which the path of the ellipfis muft be directed by a hand fupe- rior to his who only can draw an ellipfis by a tranimel or com- paffes. Of the Reprefentations of circular- and curvilinear Figures, both plain undfolid. Prob. XIX. Fig. 23. Plate XXI. To reprefent a Circle lying on the Ground Plane, or when it is Jituated in any Plane parallel to the Horizon. Operation. — Let H L be the horizon, and G R the ground line, s is the center of the pitflure, and d its diftance. Make s v equal j- d, and draw dV at right angles to dv, then will vVhe the vanifliing points to four fides of the o6lagon. Make V M equal V d. Likewife make v m equal v d, and M m will be the true meafuring points. Draw a half plan of an o6lagon, as was fliewn in Problem XVII, and Fig. 18. Make A D equal to the diameter of the given circle. Draw the vifuals 2 V, i f , inde- O o finitely. ( 290 ) finitely. Make 2 P, i / equal a q, the fide of the oftagon ; and draw from / and p meafuring lines to their refpedtive points M m, cutting at 3 and 8. From 3 and 8 drawn 3 J, 8 j. Take the fpace I D, and lay it from D to 10, and from A to 12. From 12 drawn a line to V, cutting at 7, 6. From 10 to v do the fame, cutting at 4, 5. Laftly, draw 5, 6 parallel to i, 2, and the o6tagon in which the given circle is to he infcribed is com- pleted. Method fecond. — In this method, which is very fimple, we proceed without regard to any of thofe lines ufed in the firft method, which was more fcientific, and according to Dr. Brook Taylor's fyftem. The ground plane F is fuppofed to remain as before. Let A, B, C, D, be the reprefentation of a geometrical fquare, found by the diagonals paffing to each vanilliing point, confequently S will be the center. Through S draw g c, and draw a s, from which we have four points, ij,£, e, c, of the in- tended circle. Draw a line from 2 to V, and from 10 to v, cut- ting the diagonals at /^, d, whence we have two more points. From the points If and d draw parallel lines, cutting the dia- gonals in the points b f, adding other two; which in all make eight points, fufficient for the reprefentation of the given circle. N. B. A quarter plan F is fufficient for this method. Method ( 291 ) Method third. — Draw the quarter plane of the circle to be reprefented, contained in the fquare A, E, a O, Draw the dia- gonal O A ; and from the point n, where the diagonal cuts the arch E a, raife a perpendicular to /. Reprefent a fquare as before, drawing its diagonals each way. From t draw a vifual to s, cut- ting the diagonals in the points b f. Laftly, from the points b and /draw parallels to the other diagonals, cutting at b and dy by which method there will be eight points gained as before. This laft method being fo fimple, and totally divefted of every thing that can any way perplex the learner, it has been adopted in the following problems, and in moll of the repre- fentations in this book. There are, however, various other methods of efFedling the fame thing, which might prove more pleafing to men of fcience, but which would not be fo advan- tageous to the workman, nor even to the artift, with whom fa- cility and difpatch are principal objedls. Prob. XX. Fig. 24. Plate XXI. To reprefent a Circle fittiated in a "Plane perpendicular to the Ground Plane. Operation.— Let the line R be the ground line, and L the horizon, s is the center of the pidure, and s d, on the vertical line, the diftance. Draw half the original circle B, «, C. Draw O o 2 the ( 293 ) the diagonals o D, o A ; from A and D reprcfcnt a geometrical Iquare, by drawing a line from A to d, cutting at F. From I, 2, draw parallels to 3, 9; and from 3,9, dire6t vifuals to the center j, and the diagonals of the fquare will be cut at 8, 5, 6, jy forming four points, by which the reprefentation of the circle may be corredtly drawn. Prob. XXI. Fig. 25. Plate XXI. To reprefent a Cylinder erect on the Ground Plane. After what has been faid on the preceding problem, it is fcarcely neceffary to fay any thing on this ; and therefore I fhall only obferve, that having drawn the bafe of the cylinder by the fame method as in the laft, proceed to raife perpendiculars from A, B, D, C ; and from a draw a b parallel to A B, at a dif- tance from A B equal to the original length of the cylinder. From a b reprefent another fquare, as a^ b^ c, q. Draw its dia- gonals and diameters. From the point 4 raife a perpendicular till it cut the diagonal b c. From the point 7 raife one till it cut the diagonal a q. Do the fame at the points 6 and 5, and eight points will be found at the top correfponding with thofe on the bafe, by which the cylinder may be completed. Prob. ( 293 ) Prob. XXII. Fig. 26. Plate XXI. Tojindtbe Reprefentation of a Cylinder lying on the Ground^ ivhofe Sides are oblique to the Ficlure. Operation. — Draw the ground line and horizon as iifual; and let s be the center, and d the diftance of the pi<5liire. Make J- V equal j- d^ and from cTdraw 6? V at right angles to v d, then will v\ hQ the vanifliing points of the ends and fides of the cylinder. Make a half plan of the bafe of the cylinder at <?, d, c, d^ as in the preceding cafes. Draw C A perpendicular to the ground line, and equal to the diameter of the cylinder. Draw the vifuals C v, Av, and C V, A V. Make C F equal C A, and C S equal to the given length of the cylinder. Draw F ;;^, S M, cutting at D and 3. Draw D B perpendicular to the ground line, and we have a fquare in which the end of the cylinder is to be infcribed. In like manner reprefent a fquare at the other end, as i, 2, 3, 4 ; and having drawn the diagonals and diameters of both fquares, draw parallel lines from 5, 6 to ef. From e and /dire6t vifuals to V, cutting ^ and /& ; from e, f, £\ l>^ draw vifuals to 1;, which will cut the diagonals of each fquare in four points, by which each end of the cylinder may be com- pleted. N.B. ( 294 ) N. B. A circle or cylinder may be reprefented without drawing a plan, by dividing the given diameter c a into feven equal parts, one of which will cut the diagonals as before, at leaft near enough for pradlice. Prob. XXIII. Fig. 27. Plate XXI, Tojind the Reprefentation of afemi-ellipfis^ wbofe tranfverfe Dia- meter is parallel to the Figure. Operation. — Draw the ground line and horizon as in common, and let s be the center, and d the diftance of the pic- ture. Make then a plan of the femi-ellipfis, whofe tranfverfe diameter is D G, parallel to R, the ground line. Draw A B, in- cluding half the conjugate diameter. Draw the diagonals O B, O A, cutting the elHpfis at P and N. Divide A D at K, and draw E F. From E, P, N, F, O, raife perpendiculars to the ground line at 4, 5, 6, 7, 8, 9, 10, and from each of thefe draw vifuals to s. Make 3, 2, i, each refpe<Stively equal A, K, D ; and from i, 2, 3, draw lines to d^ the diftance, cutting at a^ ^, b. From a^ X-, ^, draw parallel lines to g^lyC\ and laftly, drawn a^og, then will the feveral vifuals be cut at the points requifite for defcribing the elliptic curve, as the dotted points in the figure fhow. Prob. ( 295 ) Prob. XXIV. Fig. 28. Plate XXL ^0 find the Reprefentation of an elliptic Segment inverfely. Suppose A, B, C, D, to be the fhelf of any table, Sec. hol- lowed in front in the figure of an elliptic fegment, A, i, 2, 3,4, D. Having drawn one fide A, i, 2, 3, 4, of the given fegment at plea- fure, divide the curve into four equal parts, and from i, 2, 3, 4, raife perpendicular to a, b, c,/; then, to make the other fide of the curve fimilar to that already drawn, lay on the feveral divi- fions/, c, b, a, to the right hand, and from thefe let fall perpen- diculars at pleafure ; then, from i, 2, 3, draw parallel lines, cut- ting the correfponding perpendiculars on the right hand, by which the other half of the fegment may be accurately drawn. The plan being thus prepared, draw vifual lines to j, the cen- ter, and make r/the diftance. At a fix one foot of the com- paffes, and extend the other to i, and with it fweep the firft arch ; and in like manner fweep the arches 2, 3, 4. From the feveral points where thofe arches cut the line A D, direa lines to the diftance, cutting the feveral vifuals at the points i, 2, 3, 4. Laftly, from i draw a parallel to 7, from 2 draw one to 6, and from 3 draw one to 5 ; thus will feven points be found through which the path of the reprefented curve muft pafs. SECTION ( 296 ) SECTION V. Tlje Application of the preceding Problems to the Pracliceof Draw- ing the Reprefentation of Pieces of Archite&iirey ajid particu- larly various Pieces of Furniture in different Pofitions to the Pi&ure. The preceding problems, and the various figures referred to, muft be confidered as only laying the foundation for the re- prefentation of more compound objedls, confifting both of right and curvilinear parts. It becomes neceflary, therefore, to fliew the moll eafy application of thefe problems in a variety of examples, that the whole may appear pra6lical and ufeful, and that we may alfo fee the real effecSt of that art which we have hitherto laboured to underftand. Nor do I think that perfpec- tive could well be applied in many cafes without fuch ex- amples. Befides, the ufefulnefs of having a few proper ex- amples always ready to turn to, muft be of confequence to thofe who but feldom reprefent things in perfpecftive ; in which cafe the rules and methods will frequently efcape the memory, and make it neceflary to have recourfe to the book ; and for the fake of more readily finding the explanation of each example, the page of letter-prefs where the explanation begins, is en- graved on the copper-plate, it being a pra(Stice fometimes 1 to J%i/e'^'2 V Sh^^ti/hn. c/i^/ . Jh^m^ «.i- /^ A^ iSre^Kp %y /^ T.-rri/ ~ J?^^ ^4 '^ '^^^^2 . Mar-latv ^u/p . C 297 ) to look at the plates firft for an example of what we intend drawing. Example I. Fig. 29. Plate XXIL Haw to reprefent a receding and returning Flight of Steps wbofe Rifers are parallel to the Pi&ure. Let H L be the horizontal line, s the center, and d the dif- tance of the pi6lure; GR is the ground line. Make AB on the- ground line equal to the original length of the fleps, and draw A E perpendicular to the ground, and make the fpaces A F, F N,- N O, and O E, equal the original height of the rifers. Draw vifuals from each of thefe divifions tending to s. Draw F T' parallel to A B, and from B and T draw lines to s. Next, lay on' the ground line the breadth of the ftep^ from. B to <? ; and from' a draw a line to a' the diftance, cutting at k\ raife a perpendicu- lar from k^ cutting at n ; and from n draw a parallel to />. Thert from p raife a perpendicular to q, cutting the vifual N j- at 7 ~ draw a parallel to r, and from r a vifual to s. Then from a- to b lay the breadth of the fecond Itep, and draw a line to d, cut- ting at m ; raife a perpendicular from m to u^ and draw a line from u to J-, and a parallel from u to. w, cutting the vifual C x at? w. Laftly, lay on from b to e the breadth of the half fpace, and>from e draw a hne to d, cutting at 5, and raife a perpendi- i Pp GulajE ( 298 ) ciilar to a:, and from .v a parallel; which will complete the firft flight. The returning ftep leading to the fecond flight is next to be confidered. For this, draw the perpendicular j', 7, 8, 9, 10, at a diftance from A equal to the width of the returning fteps; draw the line 6, 7, parallel to Y A, and at 6 there is an allowance made for the bearing of the ftep ; alfo at Z there is an allowance for the other half fpace to reft on. Draw the vifuals R s and E s; and how to complete the reft of the fteps muft be evident from the figure. The returning flight comes forward until it is in the fame plane with A B, the firft rifer; therefore, after having placed the original height of the rifers at 8, 9, 10, and drawn from thefe divifions vifuals to s, it remains only to lay on the bearing of the fteps at i, 2, tending to the diftance, and cutting at 3, 4. Thefe being traced along the fteps, as fliewn by the dotted lines, till they cut the vifuals 7 s, Rs; how to perform the other part will appear obvious. N. B. The laft ftep of the returning flight 10, 12, does not all come into the plate, other- wife its length would be equal A B, the original length of the ftep. Thefe fteps might have alfo been reprefented oblique to the pidture ; but as I have not plate-room for fo many examples, the learner, muft try if. he can do it himfelf, by refledling on what C 299 ) what has already been faid and done on objecfls in obliq-ue lltu^ atlons ; but if he fail in his attempt, he may confiilt Mr. Mafc- ton's complete treatife, in its pradtical part. Example II. Fig. 30. Plate XXIL Hqw to reprefent a Tufcan Pedejlal and Bafe parallel to the Pi&ure. Draw A fir ft, the profile of the pedeftal and bafe, which i& taken from the large module of the Tufcan order in Plate VIII. Let H L be the horizon, and make j- the center, and j- d only- half the diftance of the picture, for want of room on the plate- Make G R the ground line, and on it, from B to C, lay a fpace equal to the length of the original pHnth. Draw from thefe lines to s. Next, confider how far the pedeftal is to be repre- fented from the picture, which in this example is equal twice CD; becaufe the whole diftance is equal twice s d. Therefore from D draw a line to d, cutting at F. Make DE equal halt BC, cutting at I. Draw FK and lO parallel to BC, by which a fquare will be reprefented equal to the phnth. Proceed now to reprefent the projedtion of the ©gee or bafe of the plinth. For this, take i, half the original projedion of the plinth, and place it from B to 2. From 2 draw a line to S, cutting at 3; and from 3. draw one to d, the diftance, cutting 4. Draw next P P 2. the ( 300 ) the diagonals KI, FO. From 4 draw a parallel line, cutting the diagonals at 8, 5, and from 5 draw a line to s, cutting at 6; then will be projected each miter of the plinth, and alfo the fize of the dado will be determined at the fame time. Therefore from 8, 5, and 6, raife perpendiculars at pleafure, which will ferve both for the angles of the dado and the plinth of the bafe. •From draw a line to j", which will cut the parallel produced from 8 at 5, and will give an internal miter at 5, K ; raife per- pendiculars from 5, K at pleafure. From c and 12 on the pro- file, draw lines to s, cutting the perpendiculars raifed from 5, K at/, m, which will give the correfpondent miter to 5, K. Draw the projecting diagonals of each moulding on the profile, as 9 10, II, 12, and draw ad; from all which points in the mould- ings draw vifuals to j-, which will feverally cut the aforefaid perpendiculars at 7,/', n, m^ r. Draw then the line m n^p 7, which Avill be the diagonal lines of the internal miters. Now draw parallels fvompq, which will cut the perpendiculars at 13, 14, 17. From 14, 17, draw vifuals to j-, which will cut at 15,16; and it is evident that by thefe the three miter lines will be cor- rectly determined From each angle of the mouldings on the profile draw lines to s, and afterwards obferve how the profiles are cut by each projecting diagonal, to which make every per- fpeCVive miter agree. For inftance, draw a line from v, the point where the diagonal cuts the upper fquare of the ogee, till it cut the miter line at / ; from / raife a perpendicular fliewn by the ( 301 ) the dotted line, which will form the fquare on that miter, from which the fame fquare muft be traced round the dado, as is evident from the figure, hi the fame manner muft the upper moulding be managed; which, after what has been faid, it would be a dull and tedious repetition to go through a defcrip- tion of it. And I am perfuaded, that if the learner cannot com- prehend it from what has already been faid and done on the figure, he would fail of attaining it after all that I could fay on it. It remains now to confider the bafe, with a part of the fliaft of the column : and this will admit but of very little defcription, w^hen we fuppofe the learner already acquainted with repre- fenting fqiiares and circles, of which the bafe is compofed ; and if he be not, he muft turn back to thefe, for it is impoffible to draw a figure to lliew all thefe, without confounding the whole. The principal thing to be obferved in this matter is, firft, after having drawn s, the plinth on which the bafe refts, on it a cir- cle muft be reprefented for the bottom of the torus, fomewhat lefs than the plinth, determinable from the profile ; after which the projediori of the torus muft be found, by drawing the lines b^g^ tv, to J-, cutting a parallel from the phnth L at /, X-, b. Take half k I and place it from x to sr, and a line from z to c/, cutting the vifual x j, will find the projedion of the torus, as the dotted upright line fiiews. Upon this torus mull: be reprefented a fquare, fo much lefs as the projedlion of the torus ; in this fquare a circle muft be reprefented to guide the top of the torus, ( 302 ) torus, and having already drawn one for its bottom, by thefe it may he completed. Next find the height of the fillet above the torus, which is done by drawing vifuals from the points above at; and by a fteady hand and good eye the fillet may eafil)'- be drawn, by following the upper part of the torus. Laftly, to find the projeilion of the conge or hollow ; take half k I and place it from z toy, and diredt a line to d, as before, cutting at th€ fecond upright dotted line ; how the reft is performed is only to repeat what was neceflary in reprefenting the other parts of the bafe, and therefore it is needlefs to fay more, except to obferve the neceflity of taking care in drawmg the curve lines, fo that tl\e torus may feem to reft eafy on its plinth, and not appear ta ftart fuddenly up, as is commonly the eafe in fuch reprefentations, when they are drawn by perfons who only underftand perfpe6tive, but are deftitute of tafte in drawing. Example III. Fig. 31, Plate XXIIT. How to reprefent a iufcan Entablature and Capital parallel tQ> the Figure. In the preceding example, the pedeftal, bafe, and part of the fhaft, are all under the horizon, confeqnently the returns of each moulding feem to rife up; but in the example before USj :v"2if./>/ -1 Tiisca/i JUnbib/aha-e S:c /'/a/e i^3. TSfi^r-aJi^n /}£/, ^aw-Uw f .-tify- , AiS/hcJ aj- tfit Acf Jif;,-/s /••■ ff. 7b-n: - - J)t4ir2ff-^i/^2 ( 303 ) us, every part is above the horizon, and therefore each return- ing member appears to dcfcend. Hence this horizontal line is- in a reverfe fitnation to the other, being iinder the objcdt as the hne H L, and that which we formerly ftyled the ground line,: whereon was laid each original meafurcmcnt, is now at S P, properly termed a fedtion of the picliure, on which thcfe mufk be placed. Therefore having drawn Y, the profde of the en- tablature, taken as before from Plate VIII. lay on A B the full extent of the cornice, and from AB draw vifuals toj-; divide A B at E, and draw another vifual to s. Confider then how (ar the entablature is to be reprefented from the pidurc, which in this example is equal twice EF, becaufc we have only ufcd half the full diftance. Draw then a line from F to d, cutting at G ; through G draw a parallel, cutting at I K, which will then be the front edge of the greatcft projecting part of the cornice. And fince the line from F to ^ is in a direilion only to half the diftance, it will cut the vifual A D, tending to j, in the fame point as it would be cut if a line from K was direfted to a diftance twice s cl; therefore a parallel line from D to C will reprefent a fquare equal to the whole projcdlion of the cor- nice. It is neceflary for the learner to be clear in this, other- wife he will not know what he is about, nor underftand the fucceeding directions. Having then found this fquare, draw the diagonals K D, IC, which diagonals muft neceffarily give the I proper ( 304 ) proper diredion to each miter at the top of the cornice. Take then, from Plate MIL half the upper diameter of the column^ and place it each way from E at IM N. Draw from M N vafuals to J-, which will cut the aforefaid diagonals at i, 2, and 3, de- termining the feat of the cornice, and the other mouldings. Let fall perpendiculars from the points i, 2, 3. Proceed now ta draw lines from each moulding in the profile to s the center ;^ and alfo from Q draw one to the center. Produce the parallel from I to 4, cutting the line Q. From 4 let fall a perpendi- cular, then will the vifual line O from the bottom of the cornice be cut at U. From U draw a parallel, cutting the perpendiculars from I, 2, at 6, 7 ; from 7 draw a vifual to the center j-, cutting the perpendicular from 3 at 8. Draw the projecting diagonal O 9 of the profile, and ftrictly obferve how it cuts each moidd- ing. Draw alfo U 10 of the internal mrter. In like manner draw 6, 10, 7, 12, and 8, 13. Now from the internal miter, as at e, a, b^ c, draw parallels, cutting the other i:>rojc6ling diagonals round the cornice, in the fame proportion as that of the profile. Every other particular muft be obvious from infpeilion, after what has been faid already on the pedeftal; It now remains to find the reprefentations of the architrave and capital. To do this, take the projedions /, ^, i>, from the profile, and place them from Q at /, ^, /, and from thefe direds: lines ( 305 ) lines to s, cutting the miter line near 4, as fpecified by the points. From each of thefe points let fall perpendiculars to their refpedlive vifuals already drawn ; that is, from the point neareft 4 let fall a i>erpendicurar to m, from the next point kt fell one to 0, and from the laft point let fall one tO' n, which; will find: the internal miter. From each of thefe miters dra\r parallels at pleafure, as fliewn by the figure. Laftly, thefe pa- rallels mull be cut, in order to determine the projedion of each- miter in the reprefentation, which is eafily done, by the fame method ufed in' the internal miter : thus, from M N lay on' each way /, ^, /, the fame as /, ^, /, near Q, and direft vifual lines to each miter line at i, 2, 3. From each of thefe points let fall perpendiculars as before to their refpeaive parallels, and each miter will be found, as is evident from the figure. With re- fpea to the circular mouldings in the capital, thefe muft be drawn by firft finding the fquares in which they may be in- fcribed, and then ufing that freedom of hand and good tafte, which are the befl: and only guides that can be ufed in thefe cafes. And here the learner lliould be put in mind, that the example before us not only fiiews how to reprefent the Tufcan entablature, but alfo how to draw broken mouldings parallel to the piaure, or how to reprelent a cornice round the infide of a room. For if the dotted lines drawn from the internal miter were made good and fliaded, and if thofe returning to the pro- file were alfo (haded, the efFea would then be feen. Q % .1 ihould ( 3o6 ) I fhoiild have been glad to have affifted the learner in the reprefentations of the other four orders, but he mufl be fenfible that it would be impoffible for me either to find room or time for fuch an arduous talk in a work like this, which calls for place and attention to fo many different articles. It is my opi- nion, however, that if the learner thoroughly acquaint himfelf with the reprefentation of the Tufcan order, he will not be at much lofs how to draw the other, except in the capitals of the three laft orders when they are oblique to the pi6lure. But thefe will rarely, if ever, be wanted by thofe for whom this work is intended. However, if they fliould, I will refer the reader to Mr. Malton's work, as the bell I know of, for their af- fiilance in this matter. Example IV. Fig. 32. Plate XXIII. How to reprefent Arches parallel ai^d perpendicular to the Piclure. First, of arches parallel to the pidure. Let A, B, C, D, be an arched paffage, whofe entrance is pa- rallel to the pidure, in which cafe the arch is fimilar to its ori- ginal ; that is, a perfect femicircle, as demonftratcd by Fig. 20. Plate XIX. and page 284. Therefore let the line 2, 4, drawn parallel ( 307 ) parallel to the ground be the diameter, and E the center of the arch; fweep the arch as in any other circle ; draw the vifuals A J-, B J-, and make d the dirtance. Confider next the fize of the pier or pillar on which the arch is to reft. Let A K be the thicknefs, and draw K d cutting at P. Draw P Q parallel to the ground, and raife a perpendicular from Q. From 2, 4 at the fpring of the arch, and from E the center, draw lines to s the center of the picSlure ; and the vifual line from 4 to j cutting the perpendicular from Q at 3, draw from 3 a line parallel to 2, 4, cutting the vifual Ej" at 1; then will I be the center of the furtheft femicircle, which completes the arch, by fixing the foot of the compaffes in I, extending the other to 3, and fweep- ing the arch i, 3, as the figure fhews» Example V. Fig. 32. Plate XXIIL 3o rcprefent Arches in a perpendicular Dire&ion to the Fiaure. Let the perpendicular line A 7 be the original height of the arch-way. Draw from 7 a line to the center j, and make 7, 8 equal to the femidiameter of the arch, and fromt 8 draw a line to s. Next confider how far the arch is to be front the front of the pidure, which is here equal A K. From K. Q q 2 draw ( 3o8 ) draw a line to d, the diftance, cutting at P ; and from P raife a perpendicular, cutting at lo. Take 8, 7 equal to the femidi- ameter of the original arch, and repeat it from K to N, from N to S, from which draw lines to the diftance, cutting the vi- fual A J in O Y. From thefe raife perpendiculars, cutting at 11 and e\ then will a be the center of the aixh. Draw then the diagonals a 11, a 10, and divide 9, 10, or 8, 7, into feven equal parts, and take two of thefe, as at 12 ; from which draw a line to J", cutting the diagonals, as the figure fliews by the points. Through thefe points draw, by a fteady hand, this fide of the arch. For the other fide of it proceed in the fame manner, by drawing vifuals from 2, 13. Laftly, draw a c parallel; alfo 10, 14, artd ir, 15; then from c to 15 and to 14 draw diagonals agreeing with the other, and cut thefe as before, by a line from 16, by which the other fide of the arch will be reprefented ; that is, as much of it as ought to appear. The part which does not appear is denoted by the dotted curve. In the fame manner proceed with the fecond, or with as many more arches as may be wanted, by repeatedly laying on the ground line the original meafurement at T V. Example X<>o.;,/. 2. //fuses X- (/lairs „i furs/ie,-/u re 2 4 uSfift^iz^i i*^/ 7h/-/tif/iW /if OTernf_ Aupf i. tj()'2 OJim^iff ( 309 ) Example VI. Fig. 33. Plate XXIV. Hoiv to reprefent a Houfe in Ferfpe&ive^ having its Front parallel to the Piflure. Let H L be the horizon, and G R the ground line, s is the center, and s dihQ diftance of the picture. Make AC the ori- ginal length of the front, from which draw vifuals to s. Con- fider next how far the houfe is removed back, which is here equal C i. From 1 draw a line to d^ cutting at 7 ; and from 7 draw a parallel to 8. Draw a plan of the roof i, 2, 3, 4. And from d the diftance, draw dv parallel to the fide of the roof i, 2 ; then will v be the vanifhing point for that fide of the roof. Take s v and place it below the horizon at V, perpendicular to j; then will V be the vanifliing point of the other fide of the roof 2, 3. From 8 and 7 raife perpendiculars at pleafure, and make A F the original height of the front. From F draw a line to j, cutting at 9 ; draw a parallel from 9 to 10. For the windows and door, lay their original meafurements on A F and A C, drawing vifuals to j, as the figure fliews ; and as the front is parallel to the pidurc, confequently each object on it is fimilar to their originals ■••, and therefore lines perpendicular to 8, 7, * See pages 274 and 27J. I and ( 310 ) and 9,8, will form the fides, tops, and bottoms of each window and door-way. From 9, 10 draw lines to ^', the vaniflring point of the roof; from 10 draw a line to s, the center. Take then I, 3, the fpan of the roof, and place it from F to B ; and from B draw a line to j", cutting at 11 ; from 1 1 draw a line to V, be- low the horizon, cutting at 14; from 14 draw a parallel to 13, for the top of the roof; and from 13 draw a line to V, cutting the line 10 s at 15, forming the fartheft fide of the roof; draw a perpendicular from 15 to 6, which w^ill complete the end of the houfe. Laflly, to find the height of the chimney, draw a line from s through 14, cutting at E ; and from E lay on the original height of the chimney to D ; and from D draw a line to J-, cutting a perpendicular from 14, which will give the height required. Method fecond. — The front of the houfe being drawn as has been defcribed, to find the appearance of the roof and gable- end, draw the roof i, 2, 3, as before; and from 4 and 3 draw lines to d, cutting at 5, 6; from 5, 6 raife perpendiculars at plea- fure ; from 5 draw a parallel to O, cutting the vifual A j- at O, for the center of the left gable-end ; from O raife a perpendicular at pleafure. Take then the perpendicular height of the roof, from 4 to 2, and place it from F to E; and from E draw a line to s, cutting the aforefaid perpendicular at 14, which will give both the ( 311 ) the pitch and height of the roof. From 14 draw a parallel to 13, cutting the other perpendicular corrcfpondent \vith 14. Laftly, from 9 draw a line to 14, and from 10 draw a line to 13, and from 13 to 15, which will determine the appearance of the roof, as before. Example VII. Fig. 34. Plate XXIV. "To find the Reprefentation of a Hoiife zvhofe Gable-end is parallel to the PiHure. In this cafe the front that was before paralLl to the pidture is now turned perpendicular to it. The gable is therefore pa- rallel to the pi(5lure, and is nothing more than a geometrical elevation, found by laying on the heights on a b, and the widths on a f, and drawing lines from thefe to j, the center; w/ is the diftance of the houfe from the pi(5lure ; and a line from 7n to </, cutting at ;z, finds the reprefentation of that dif- tance. The other lines to the left of m, all tend to d alfo, by which the windows and doors. Sec. are found ; m q is equal to the original length of the front, a line therefore from q to d de- termines its apparent length on the picture. For the pitch of the roof, draw ^ j, cutting at/); from which raife a perpendi- cular ; draw another perpendicular from w, the center of the other ( 312 ) other gable-end; alfo draw the vifiials k s^ /s, for the roof; which vifuals will cut perpendiculars at b and /, anfwering ta the points / /^, by which the roof is formed. For the reft, the figure itfelf is fufficient, by obferving that ti t is the perpendi- cular height of the roof, and / ^ of the cliimiiey. Example VIII. Fig. 35. Plate XXIV. How to reprefent a Chair, having its Front parallel to the PiSIure^ After having made a fcale of feet and inches to propor- tion each part of the chair by, draw A, the profile of the back and fide rail; and draw B on the right, according to the bevel of the feat; and obferve, to diftinguifli the fines of each chair, one: is marked with fmall letters, and the other with numerals. Let H L be the horizon proportioned by the fcale, about five feet high from G R the ground line. Make a b equal to the length of the front ; from which draw lines to j, the center,, which, in general, ought to be perpendicular over the middle of the chair, becaufc it affords the moll: eafy and natural vievv of its back. Next, from q, the width of the feat, draw a line to the diftance, here out of the plate, cutting the vifual a s ^X c ; from ( 3^3 ) ■ from c draw a parallel to e at pleafiire. Take C D, the bevel of the feat, and place it from a to d; and from d draw a line to j, cutting c e at y, which gives the bevel of the feat. From a draw aline through jk, cutting the horizon at V, which will be the vanifliing point to every line originally parallel to ay, the fide rail ; take s V and place the fame fpace to v, M'hich will be the vanifliing point to the other fide of the chair; therefore from If draw a line to v, cutting at e, which forms the feat. For the thicknefs of the back rail, draw a line from p to the diftance, as the figure fliews. For the height of the back, raife a perpen- dicular a gy and draw a parallel from r to ^ ; draw alfo a per- pendicular from J', and a line from g to V will cut it at 7^ de- termining the height of the back. For the bottom of the back foot, draw a line from u to the diftance, cutting a per- pendicular from c at w. From w draw a parallel, and from z draw a line to the vanifhing point V, cutting at .v, which will determine the place of the back foot '■ . How every other part is done, muft be evident from infpe<5ling the figure. * The reader will perceive that the line from z to *• is not accurately drawn, for the engraver did not follow his copy, otherwife the line would have touched the bottom of the back foot tending to V, which the learner may prove, by drawing a line from z to V. This inftance may ferve to (hew the trouble there is with engravers, who in general are totally ignorant of perfpeftive. R r Example ( 314 ) Example IX. Fig. 36. Plate XXIV. How to reprefent a Chair having its Front perpendicular to the Pi&ure, In this example the fame ground line, horizon, center, and diftance, is ufed as in the preceding ; therefore let the fpace 7, i, be equal to the length of the chair front. From 7 draw a line to J, and from i draw a line to the diftance, cutting at 16. Make 7, 9 equal to the length of the fide rail, and from 9 draw a line to j; make 9, 10 the thicknefs of the back foot, and from 10 draw a line to j, as before. Draw a parallel line for the depth of the fide rail, and from 8 draw a line to s. Next con- lider how much the back foot fweeps off from the perpendicu- lar, which is equal to the fpace 12, 13, or 2,22; draw vifuals from each of thefe points, as the example directs. To find the bevel of the fides, take C D and place it from 7 to 5, and from i to 3; from which draw lines to the diftance, cutting at 11 and 17; from II and 17 draw parallels cutting the vifual 9 j at 20 and 18; from 7 draw a line to 20, and from 16 draw one to 18, which will finifh the outline of the feat. Laftly, from 18 and 20 let fall perpendiculars, cutting at 24, 25 ; from which draw parallels to the vifual 13 j, which gives the bottom of each -Vf./ pi g M rtate.2.i. .'/nrff.i I /I Jif /u/ifcli^iM,- ,>er f^Jr/i/(t/niiii'ii /"'J'"' ■ {t ^ rrn ntrae r.r/trr,jrfn /]<! -Liiihj/ied III- the AcCiiirects. bv G Terry October I'qi. Mtlf^Sculfi C 315 ) each back foot ; and for every other particular, a little reflec- tion and obfervation will be fufficient. Example X. Fig. 37. Plate XXV. How to reprefent a round fable in Perfpe&ive, having two of its Claws in front parallel to the FiHure. Draw a profile of the pillar and claw, as at A. Take a by the fpring of the claw, from the center of the pillar, and with it defcribe a circle 1, 2, 3; divide the circle into three equal parts, fo as to fuit the intended pofition of the claws, as i, 2, 3; draw from thefe perpendicular lines to /, e^f Reprefent a fquare 4, 5, 6, 7, equal to the diameter of the top; draw the dia- gonals and diameters of the fquare, and from //draw vifuals to s ; from C, the center, draw a perpendicular for the pillar ; and having determined the height of the table at B D, from B D reprefent a circle for the top, as has been taught in page 289, fee Fig. 23. Next find the place of the claws; for which make f e equal/ 2, and from e draw a line to the diflance d^ cutting at g\ from g draw a parallel to h^ for the other claw. To find the place of the back claw; extend the compaflTes from e to 3, and make 4 c equal to it; from c draw a line to the diflance, cutting at m ; and from m draw a parallel to /, which will be the place Rr2 of ( 3i6 ) of the claw. For the different parts of the pillar, draw from the profile lines to the diftance, cutting the perpendicular C F, as the figure fliews. It now remains for every part to be finiflied by a good hand and eye accompanied with judgment, as no other rwles can be of any fervice in cafes of this fort. Example XI. Fig. 38. Plate XXV. How to reprefefit an oHagoti Table having one of its Claws in Front perpendicular to the Pi&ure, Draw the profile of the pillar and claw, as at B ; and, as in the other example, take the fpring of the foot or claw from the center of the pillar, and with it defcribe a circle, and mark, out the place of the claws at i, 2, 3. Draw i, 2, 3 up to the ground line, and produce i up to «, for the height of the table. Reprefent a fquare both at top and bottom, and draw the dia- gonals, finding the center for the pillar. Draw now the dotted lines from the profile to k u the perpendicular, and where they cut draw lines to s, the center of the picflure, cutting the center of the pillar for each refpedive moulding. Next find the fitu- ation of the claws ; having drawn lines from k^ h, a, to j-, make b b equal h /; and from b draw a line to the diftance, cutting at ^, which will be the place for the firfl: claw. Make a c equal a 3, and from c draw a line to d^ as before, cutting at b ; from b draw ( 317 ) draw a parallel to <?, then will 3 ehe the i^lace of the two other claws. From 5 and 4, produced from 7, the height of the toe draw lines to s ; and from e and l> raife perpendiculars cutting thefe, which will be the height of the toes of the back claws. Laftly, we here fuppofe the top to be an irregular odlagon, wherefore let mnhQ equal to four of its fides ; draw from n m lines to j-, from n draw a line to d, cutting at ; from draw a parallel to t\ finding the oppofite angle, draw mt\ and from the diftance draw a line through w, cutting at r ; from r draw a parallel to p ; and draw p q, which will finilh the o6lagon for the top. Example XII. Fig. 39. Plate XXV. To put a Commode 'fable in Perfpeclive, having its Front pa- rallel to the Figure. Observe, the ground line for the tables is here ufed as the horizon for the commode. Make s d half the diftance, for want of room on the plate, and make G R the ground line. Draw then the plan P of the front, according to the intended fcale. And, in cutting of each vifual line, ufe one half of a foot inftead of a whole one; be- caufe only half the whole diftance is ufed. Therefore, having drawn ( 3iS ) drawn the vifuals 3 J', B j, draw a line from i foot on the fcale hne to d the diftance, cuttmg at g\ then will 3^ reprefent a line two feet long, equal to the breadth of the commode. From g raife a jjerpendicular, cutting at ;;;, finding the apparent width of the top ; draw 5, 10 parallel and equal to the height of the foot and bottom of the commode ; draw parallel lines, alfo, for the partition below and above the drawer, and for the top^ as fliewn by the figure. Proceed now to find the place of the feet and the fweep of the front : for the feet take half 3, 4, and from 3 place it to 6 ; from which draw a line to d, cutting at 2 ; from 2 draw a parallel cutting B J, for the other foot. Find now two points by which to direct the fweep of the front thus : draw perpendicular lines from the plan at 9, 12, and from 13, /, /-, where they cut, draw lines to s ; then take half 8, 9 and place it from kto i; and from / draw a line to </, cutting at />, finding a point for the curve ; from p draw a parallel to /, finding the oppofite point, which will be fufficient for the whole. Lafl:ly, for the recefs draw vifuals from ;•/, and, fuppofing the recefs to be a foot deep from front, make ^/ equal half a foot on the fcale ; draw from e a line to d^ cutting at ; and from draw a parallel to the oppofite vifual. Every other thing may be learned by obfervation, without going through a minute detail of every particular, which would become an exceeding dry tafk indeed. Example C 319 ) Example XIII. Fig. 40. Plate XXVI. How to reprefent a Chair obliquely fitu at ed to the Pi&ure. In the two former examples of chairs in perfpecflive, the firft of thefe had its front parallel to the pidure, which is the moft ufual way of reprefenting a chair when it is wanted to be viewed as a pattern ; for the back being parallel alfo, it gives the moft natural and diftindl view of the banifter and all its parts. The fecond is put with its front perpendicular to the picture, which is a pofition wanted in the reprefentation of in- ternal views of rooms or paffages : and this third example being put oblique, is conlidered by painters moft pi(5lurefque or fuit- able for a pi6lure, in which cafe the pattern of the chair is not much regarded, only its unformal fituation fuiting to the fub- jedt and circumftances of the defign. In this example I fhall therefore confider myfelf as offering fome alliftance to the painter, as well as in a few other inftances in this book. Obferve, that the vanifhing points "uV, and meafuring points »z M, of this example, are all found by laying the dif- tance downwards to D, for want of room on the plate, and which needs not here be explained, after what has been done 7 in ( 3^0 ) in problem VI. page 236, as it makes no difference whether the diftance be above or below the horizon. Therefore proceed in confidering G R the ground line, drawn parallel to the horizon H L; on G R make a fcale of inches to proportion every part by. Make ^/ equal to the original length of the front, which in parlour chairs is generally 21 or 22 inches; and let aghQ equal to the width of the feat from the infide of the back to the front, commonly 16 inches. A.s a is confidered the nearefl angle to the picture, from a raife a perpendicular at pleafure, on which the original heights of each part muft be laid, as from a to w, for the height of the feat rail, about 16 inches without the fluffing. From a and w draw vifuals tend- ing to V and v. From fc draw lines to m, cutting at xy; from If do the fame, cutting at 3 ; from which points raife perpendi- culars for each foot. Next, from g draw a line to M, cutting at k; from which raife a perpendicular to ; from draw a line to V ; and from 4, the infide of the front foot, whofe thicknefs is fuppofed equal to the bevel of the fide rail, draw a line to v, cutting at p ; then from w, the outfide of the foot, draw a line to /), produced till it cut the horizon at 0, which will be the va- nifhing point to every line originally parallel to the fide w p. From V extend the compalTes to 0, which lay on to O, and O will be the vanilliing point to all lines parallel to the other fide / 5. Therefore, from / draw a line to O, which will cut at 5, com- pleting the form of the feat. On the perpendicular line from w, lay _F/<jff 2/^. See. A^ z'n /l. J'^/ ^ ■A" V ^^rr.^^. \.J' T^Sh^r^eUcn. t&Z /iiS&yfiaJ tfj tJ^ ./.</ ./f/et-tt fir r Sficr-a/crt J^^vT Mf., t^9-' ( 3^1 ) lay on 21 inches for the height of the back, and diredt a hne to 0, and through/) draw a perpendicular at pleafure for the joint of the fide rail. Next confider how much the back foot pitches which in this example is equal b g, and b i is for the thicknefs of the toe. From thefe draw lines to M, cutting at k^ /, n ; and from k^ /, Hy draw lines to V, which will cut the vifual b v in the place for the toe at 8, 6; from 6 raife a perpendicular cut- ting at 7, and from 7 direct a line to V, for the top rail ; and how the reft is performed muft be obvious from what has al- ready been faid and done. Example XIV. Fig. 41. Plate XXVI. To put a Cylinder Dejk and Book-cafe in Perfpe&ive^ having its Front oblique to the Pi&ure. Draw firft an elevation of the cornice and pediment, and proportion the pediment according to Fig. 36, Plate V. by di- viding half the length of the cornice into nine equal parts, of which take four for the pitch. Take one of thefe parts for the height of the pedeftal, and the remaining three for the vafe. Draw lines up to the ground line at 7, r, F, />,/, and the vanifh- ing points having been already found, draw from r lines tend- ing to each; from r, the neareft angle of the book-cafe, raife a S f perpendicular ( 322 ) perpendicular at pleafurc, on which the feveral heights muft be laid. From r to A lay on the depth of the lower part, and dire6l a line to M, cutting at U, and make A B the depth of the book-cafe, and draw a line as before, cutting at X, from which raife a perpendicular. In the fame manner draw lines from F/>, tending to ;«, and cutting at 3, 12, for the length and center of the book-cafe. The feveral original heights for the defk part, doors, and cornice, muft now be placed on the perpendicular, from which lines muft be drawn to each vanifliing point. And here we muft obferve, that as the neareft angle of the book-cafe comes forward to the pidlure ■■'••, confequently the Aider is on this fide of it. To projedt the Aider in this cafe, a vanifhing point muft be found, from which, if a line be directed it will pafs through the diagonal of any fquare. Thus : on D, the dif- tance, fweep the arch S, and bifed: it at S, and through S diredt a line to the horizon, cutting at d on the fmall drawers ; lay from r to ^ a fpace equal to the projedlion of the Aider ; and from g dire<St a line to m^ cutting at / ; from / raife a perpendi- cular to ^; and from ^, the aforefaid vanifliing point, draw a line through^ at pleafure; and from v draw a vifual for the end of the Aider, cutting at «; from n draw a line to V, and from V draw one through 10, for the other end of the Aider. The opening of the door is next to be confidered. It is evident * Wlien any objedl is reprefented to touch the ground-line, that part which touchej it is fiud to be iu the pidture. 7 that ( 323 ) that a door turning on its hinges muft defcribe a femicircle, and therefore if a femi is reprefented, whofe radius is equal to the breadth of the door, its circumference will determine any open- ing that can be propofed. To defcribe the femicircle proceed thus. — From the vanifh- point V draw a line through z, the center of the book-cafe, and produce it at pleafure ; then from d, the vanifliing point of any diagonal, draw a line through 12, cutting at C ; from C draw a line to V ; and from v draw a line through 12, cutting at K ; and from K draw another diagonal to d, cutting at w ; from v draw a line through w^ cutting at E, and produced to Q, cutting a parallel from C ; from 12 to E draw a diagonal, and if the door is intended to be opened 45 degrees more than fquare, pi-o- duce this diagonal, as fliewn by the dotted line, till it cut the horizon, and its interfe6tion with it will be the vanifhing point for the top and bottom of the door. Divide C Q into feven equal parts, and from one of which at 7 diredt a line to w, cmt- ting at 13; and from 13 draw a vifual to v^ cutting at i ; from I draw a vifual to V, cutting the other diagonal at 2 ; from 2 raife a perpendicular for the apparent breadth of the door in this pofition ; and from the laft mentioned vanifliing point found by the dotted line, draw lines for the top and bottom of the door, by which it may be completed. For the ends of the cy- linder we need not fay any thing, as this is the fame as in pro- S f 2 blem . C 324 ) blem XXII. therefore we fhall proceed with the cornice and pe- diment. Set off the projeilion q r of the cornice at 6, 5, on a parallel line drawn at the full height of the book-cafe, and drasv lines to V, and the line 5 will cut the perpendicular raifed from X, and the line 6 will cut a perpendicular at 8, fuppofed to be raifed from /, the miter point of the cornice, which is found by drawing a line from «', the vanilliing point of the diagonal to X, cutting at t\ fi"om t dire<5l a line to V, cutting at ^; and from a raife a perpendicular, which will cut a line drawn from 8 to V, at the other miter point ; every other part of the cornice muft be finiflied by the reader's judgment, governed by thefe prin- ciples, as it would be impoflible to apply every rule in fuch fmall examples. Laftly, for the pitch of the pediment, a vanifhing point muft be found, according to the principles in Problem IX. Plate XVI. by drawing a line from m parallel to the pitch line at the elevation P, produced to VP, cutting a perpendicular from V; from 8 draw a line to V P, cutting a perpendicular in the center of the front edge of its cornice ; from which draw the other lide of the pediment, which, if produced, would cut a point as much below the horizon as V P is above it. Thefe pitch lines being found, the fcroll pediment may be drawn by hand with fufficient ( 325 ) fufficient accuracy; but if the pediment be a ftraight pitch, then the lines for each moulding muft tend to V P, and to a point as much below the horizon. And I would here obferve, that in drawing after thefe examples, it is not intended that the dif- tances made ufe of in them iliould be a precedent to the learner. Thefe are chofen to fuit the plate ; but the learner having fuf- ficient room on his drawing-board, muft choofe his diftance to give the moft natural and pleafing effedt to his drawing, by the rules already laid down. See page 275. In thefe examples almoft every difficult part of perfpeflive is introduced, and it is prefumed that, after the learner has made himfelf fully mafter of them, nothing will occur in prac- tice that can give him much trouble, efpecially if he be pro- perly acquainted with the fhort theory that has been given. However I am fully perfuaded, that no cabinet-maker or up- holfterer will ever want to pradlife more ; and, if I am not mif- taken, there are but very few painters who are at the trouble of pra6lifing fo much. But if the reader's profeffion or neceffities fliould require him to extend his fkill in this art further than what has been advanced in this treatife, I will freely refer him to. Mr. Malton's complete Treatife, from which, it is here gratefully acknowledged, 1 have received coniiderable affiftance. SECTION* ( 326 ) SECTION VI. Containing a JJjort View of the Nature and Principles of Shadows^ caufed by the Sun coming in different Directions to the Pic- ture \ together with fome Remarks on the Eff'eH of Light and Shade in general. What has hitherto been done in the foregoing feclions is termed by artifts linear perfpedtive, which propofes rules for drawing the outlines of objedls in every fituation, proportioned one to another according to their magnitude and diftance from the pidture; but the fubjecl of the prefent fedtion is to propofe rules for giving efFed to thefe outlines, by the different cir- cumftances of light and fhade. The mere outlines of a draw- ing is but as a fkeleton without flelh or life, but by the addi- tion of proper light and fhadow, we may almoft behold nature in a picture : and that which before appeared flat and infipid, now obtains the force and effetSl of the objects themfelves. The dodlrine of hght and fhadow may be confidered under three heads. As, Firft, when the force of the fun's rays fall on objects, and thereby produce a Ihadow ftrongly defined. Secondly, ( 327 ) Secondly, When the fun is not fuppofed to fhine, and the fhadow is only produced by light fimply confidered, or by reflediion. Thirdly, When the light or fhade of one objefl is propor- tioned with that of another at a greater diftance in the fame picture. This is termed the aerial part of perfpedlive, or the diminution of tints according to the diftance of objects. The firft of thefe heads is, however, that which principally concerns us, it being reducible to ftridt rules ; the fecond fol- lows of courfe ; and the laft can only be learned by obfervation and practice. In confidering the fhadows caufed by the fun's rays we may obferve the following diftin6lions. Firft, When the fun's rays are in the plane of the pi6ture, or, which is the fame thing, when they are confidered parallel to it. Secondly, When the rays come from behind the pidlure. And, Thirdly, When they have their dire<Stion from the front of the pidture. Case ( 3^8 ) Case I. Fig. 42. Plate XXVI. To proje& the Shadows of Obje&s in various Pojitions when the Sun's Rays are parallel to the Pi&ure, The fun, which is the great fource of light, being at an immenfe diftance from the earth, the rays of light iffuing from it in right-lined dire<5tions, are confidered as parallel to each other. The truth of this is proved by the parallel fhadows which it always produces on a plane from objects which are parallel to each other and of equal thicknefs. When, therefore, the rays are confidered as parallel to the pidlure, the fliadows of all objeds are found by parallel lines pairing by the angles of each objed, and in fuch a degree of inclination as the fun is fuppofed to be in, either to the right or left of the center of the pi<f^ure. Thefe lines, reprefenting the fun's rays, being cut by lines from the bafes of each object drawn parallel to the ground-line, find every fliadow in this cafe. The learner will recolledl, that in ftating the theory of lines parallel to the pidture in page 215, it is there faid, " Lines " which are parallel to the pidture can have no vanifliing line or ( 329 ) " or point in it, becaufe if infinitely produced would never " cut it." The fame holds good in the theory of fhadows when the fun's rays are parallel to the pi6lure ; for then they cannot cut it, and confequently a vanifliing point is not wanted in this cafe. Hence the fliadows of all lines perpendicular to the ground are drawn parallel to the ground line ; and as, in perfpedtive, all lines perpendicular to the pi6lure vanifli into its center, fo likewife the Ihadows of every fuch line will tend to it. There- fore, Example I. Fig. 42. Suppose A to be the reprefentation of a wall perpendicular to the ground and to the picSture, R R is a ray from the fun in- clining to the left in an angle of forty-five degrees, therefore the fliadow 2, 3 of the perpendicular line i, 2 is equal in length to the line itfelf. Draw the other ray r r parallel to R R, and the fliadow r will be equal to the height of the wall r. The line I r is originally perpendicular to the pidture, and vanifhes in j-, the center ; fo is its Ihadow 3 r, which likewife tends to it. T t Example ( 330 ) Example II. Fig. 42. Suppose EB an objedt any where on the ground, whofe fides EB are oblique to the pi6lure. Draw through each angle a ray rr parallel with RR the given one, and draw lines from the foot of each perpendicular, as 4, 6, parallel to the ground line, and their fedlions with each other will form points for the outline of the fhadow. Laftly, from the point 5 draw a line to 7, and from 7 draw one to 8, and filling it up, the fhadow will be completed. Obferve, the line 4, 9, and its parallels, are not perpendicular to the picture ; therefore its fliadow line 5 7 does not tend to s the center, but to the fame vanifliing point necelTary for draw- ing the fide B. In the fame manner the fhadow line 7 8 vaniflies to the point requifite for drawing the fide E. Example III. Fig. 42. Let D be an objed: having the fide D inclined to the hori- zon, and the other fides oblique to the picture. Draw a ray through ^, and through /parallel to the given ray RR ; from^ the foot of b^ and from d the foot of/, draw lines parallel to the ground ( 331 ) ground line, which will interfe6t the rays at a and c. To com- plete the fhadow, draw a line from the extremity of the inclined plane to a^ and from ato c» Example IV. Fig. 42. Let F be the flump of a column refting on one end, whofe fhadow is required. Find the diameter of the column each way, both at top and bottom, as the figure fliews ; and through the extremities of thefe diameters draw parallel rays as before. Lallly, from the foot of each perpendicular falling from the center and diameter, draw hnes parallel to the ground line, cut- ting the rays at v^w^X', draw a curve to pafs through thefc three points, and the fliadow will be projected. Thus it is evident how eafy a matter it is to projed: the fhadow of any kind of obje6l when the rays are parallel to the pi(5ture, and when the fliadow is to fall on the ground plane, as in the foregoing examples. It is, however, fometimes neceflary to projecSt fhadows fall- ing on other objects contiguous to thofe whofe fhadows are re- quired. Therefore, Tta Example ( 332 ) Example I. Fig. 42. Suppose the objecfl D ftanding in the way of the fliadow of A, a plane of r^ys palling by the end i, 2 of the wall, will make a fe6tion of D at /, /, 3; which is found by drawing the line from 2 through to 3, and from 3, where it cuts the ray R R, raife a perpendicular to /', and from / draw a line to /, which will determine how far the fhadow comes in front. Laftly, the bafe line t d^ of the object D, cuts a line from 3 at ^; therefore, from e raife a perpendicular correfponding with 3 /, and from / draw a line to the aforefaid perpendicular, and the fhadow, fo far as it afFe<fls the inclined plane D, will be found. Example II. Fig. 42. Suppose the objed: C near fome inclined plane G, whofe fhadow falls upon it. To find the fliadow, draw a line h to G, parallel to the ground line, at pleafure; draw then a ray, as before, cutting at G, where the fhadow would have terminated if the inclined plane had not been there ; draw m /parallel to n 0, cutting the ray at /) ; do the fame at the other end, and the fhadow will be completed. Before ( 333 ) Before I enter upon the other cafes of Ihadows, I would here remark, that this which has now been exemplified is, in my opinion, the moft ufeful, as well as moft eafily pradlifed. Particularly it is the moft ufeful to the cabinet-maker and up- holfterer, who only want it for fhading different pieces of fur- niture; becaufe the fliadows thus proje6led will be to the right or left of the piece, according as the light is fuppofed to come in; but in the two following cafes of the fun's rays, the fhadows will be projected either behind, or onthe front of the piece of furniture, which fituations of lliadow are liable to the following obje6tions. Firft, if the rays come from behind the pi(5lure, the front of the piece will be all in fliadow, and confequently the effe£t of diftindtnefs of parts, wliich is always expelled in furniture, will be deftroyed. Secondly, if the rays come on the front, then the fhadow will be behind the piece, and therefore little or none of it will be feen, unlefs the point of light be taken very low, which is not very agreeable. Befides, the light coming thus ftrong on the piece, leaves a glare on the front that does not produce a pleafing efFedt in furniture, nor fufHciently diftinguiflies the front from the white ground of paper on which it is generally drawn. Painters, ( 334 ) Painters, indeed, are faid to make this laft-mentioned pofi- tion of light to the picTtiire their choice, becaufe, I fuppofe, it clears their picture from the appearance of long black fhadows, which would frequently look too harfli, and introduce confu- fion, as is the cafe when the light comes in from behind. Yet as every cafe of fhadowing may be neceflary at times, though not out of choice, I fliall therefore proceed to the fecond cafe propofed. Case II. Fig. 43. Plate XXVI. To prqje& the Sbadoivs of Obje&s tuhen the Rays come in a Direc- tion from behind the Figure. When a ray of light comes in a diredtion not parallel to the pi6ture, it will neceflarily cut it in fome point in the hori- zontal line, or vanifliing line of the ground plane ; for the fun being at an immenfe diftance, and the plane of the horizon being confidered as infinitely extended, we may fuppofe a per- pendicular let fall from the place of the fun will touch fome- where on the horizon. And hence, the point where it touches the horizon is the vanifhing point of the fhadows, and confe- quently a line drawn through the faid point perpendicular to the horizon will be the vanifhing line of the fun's rays ; and any where on this line, if a point be fixed according to the fuppofed 6 altitude ( 335 ) altitude of the fun, it will be the vanifhing point of thofe rays. Thus : — in Fig. 43, the center and diftance of the pi6ture remaining the fame as when ufed for drawing the cube, let it be required to find its fhadow when the fun's inclination to the left is thirty-two degrees, and when its altitude is forty-five. From ^, the diftance, draw the line dh^ inclining from the per- pendicular J ^ in an angle of thirty-two degrees ; and through h draw S S perpendicular to the horizon ; then will S S be the va- nifhing line for the fun's rays. Make ^ M equal /6 6?, and from M draw M S, making an angle with the horizon equal to forty- five degrees ; then will S above the horizon be the vanifliing point of the rays when the fun comes from behind the pidlure, and S below it will fupply its place when the rays come on the front. From the vanifliing point h of the fhadow draw lines through the angles i, 3, 8, of the cube ; and from S draw lines through its upper angles 2, 4, 9, interfedting the lines drawn from h in the points 5, 6, lo; from the point 5 draw a line to 6, and from 6 a line to 10, which completes the fliadow. Obfervations on the 'Theory of the above Figure. The rays S 6 and S 10, forming a triangle, may be confi- dered as a plane of rays pafling by the angle 4, 9 of the cube, and ( 3?>(^ ) and being ftopped on the ground plane at 6, lo, occafions a Ihadow up to the cube, which fliadow will vanifli in the line 6, 10, to V; becaufe the angle or line 4, 9, which projected it, was drawn to and vaniflies in V ; confequently a line from V to S, the fuppofed place of the fun, will be the vanifliing line of the faid plane of rays. The fliadovv on the other fide is com- pofed of two lines, becaufe it is projedled by two lines in dif- ferent pofitions to each other. Thus the line' 2, 4, originally parallel to the horizon and to the ground, proje<5ls the fliadow line 5, 5 by the plane of rays 5, S, 6 ; which fliadow line 5, 6 will vanifli in V, becaufe the angle or line 2, 4 vaniflies there. The fhadow line 5, i is projedled from the perpendicular line i, 2 by the plane of rays 5, ^, S, pafling by the angle or perpendicular line I, 2, and therefore the fliadow line 5, i will vanifli in h, the feat of the luminary on the pidlure ; through which a line S S pafling in a perpendicular diredlion to the horizon, anfwerable to the perpendicular fides of the cube, is the vanifliing line of the plane of rays 5, S, h^ in the fame manner, and for the fame reafon, as the horizontal <u V is the vanifliing line of the flia- dows of lines originally parallel to it. The vanifliing line S S of the fun's rays may be fuppofed to move along the horizon anfwerable to the fun's inclination to the right or left of the center of the pi6lure s, whether the fun be fuppofed on this or that fide of the picture, or as we conceive of it by the figure, whether it be above or below the horizon. Hence, if a plane of ( 337 ) of rays be Jlippofed to come from behind the pi6liire, in a di- redtion perpendicvilar to it, the place of the fun will be fome- where on a perpendicular line drawn through the center of the picture, as S d. And this place of the fun, or, which is the fame thing, the vanifliing point S, of its rays, will be above or below the horizon, according to the fuppofed altitude of the fun. If, therefore, we imagiiie the fun's altitude to be as before, its place will" be at d when -the fun is behind the pidure, and at S when it is before it ; arid the vanifliing point of the fhadow will be at j, the center of th« picture. This is evident, for the angle V, d^ y, is the fame and equal to M, S, ^. In both cafes the lines /?* S, od:, of the angles of the fun's altitude are the fame, being equal to the diftance j-V of the picflure : for, in the fliadow' of the cube, when the plane of rays from behind the pidture' eutit in the oblique diredtion of the line db, the line dh is then' cbrilidered as the diftance of the pi6lure, and being turned up to S, is equal to the dillance of the place of the fun above the horizon. And fuppofe the rays to come to the picture in the dire6liori of d v, then b would be moved to v, and v d would be equal to the diftance of the pidture ; and being turned up to v S, S would then be the place of the fun, or the vanifliing point of its' irays, and v the vanifliing point both of the fhadow and fide of the cube 2, 4. In which cafe we fliould only have the fliadow of the fide 4, 9, 3, 8. Uu It ( 338 ) I It is further obfervable, that as the fun may be fuppofed to move in a circle, and if that circle be defcribed by a radius equal to the diftance of the pi(5ture, we may fhew the different fhadows of the fun upon objedls at the various times of the day. Thus : — in Fig. 44, fuppofe a line drawn from E W forming the horizon ; from the center s defcribe a circle with the dif- tance of the pi6ture, and through s draw a hne perpendicular to the horizon, and M will be the place of the fun at noon. Now let it be required to find the morning fhadow of the rod a when the fun has rifen 40 degrees above the horizon, as at 4o''S. From 40" S let fall a perpendicular to the horizon at -6, and draw it through to the other femicircle ; from i*, the vanilhing point, of the fhadow, draw lines pafTmg by the bottom of the rod at pleafure; and from 40° S, the place of the fun, draw a ray through a^ the top of the rod, cutting at i ; which fhews the length of the fhadow required. Suppofe the fliadow of the fame rod be wanted at noon, s will then be the vanifhing point of the fhadow, and M the vanifliing point of the fun's rays, and the length of the fhadow will be at 5. Again, if it be required to find the fhadow of the fame rod after the fun has palTed the meridian 50 degrees, this will bring the fun to the fame degree in the afternoon as it was in the morning ; and by drawing lines 6 in ( 339 ) in the fame manner as in the morning, the Ihadow in the after- noon will be at 2. Now, if the fun be conjGdered on this lide the picture, the Ihadows of the fame rod a, at thefe different periods of the day, will be refpedlively beyond the rod at 3, 4, 6, towards the hori- zon ; which is done by tranfprojefting the place of the fun to SMS, and drawing rays from the top of the rod to each place of the fun. Thus : from a draw the dotted line to S on the left, cutting at 3, and 3 will be the length of the morning fliadow ; and from a draw the dotted line to S on the right, cutting at 4, which will be the evening fliadow. Laftly, a dotted line from a to M, cutting at 6, will be the fliadow at noon, which is hardly feen on the pidlure. Thus we fee that the fliadows of a morning or evening view are long, tending oppoflte ways; and thofe of a view reprefenting noon-day are fliort, tending from fouth to north, nearly fo. But if we lived in a meridian on the line, then it is evident that at noon there would not be the leafl: fliadow of objects of equal thicknefs fl:anding perpendicular on the ground: for, fuppofe the rod a moved into the line M M, then the obje(5t would be in the fame plane with the rays of the fun; and being diredly under it, of courfe all fliadow would be excluded excepting fufpending obje(51;s, as No. 2, and thofe fupported like tables ; in which cafe the rays ;• r faJIing perpendicular to the U u 2 ground, ( 340 ) ground, and parallel to each other, on accoiint of the fun's great diftance, they would form a cylinder, of which the flia- dow would be a parallel feition, and therefore muft be perfedtly iimilar to the object itfelf,both in magnitude and form, as muft be evident from the figure, and a little refiedtion. .on. theijfbre- going principles. iftoq'lo-i 2d Iliv/ '" <'■'■: tiff ;nOv^ ^ASE III. , Hsl^diio 'fo find the Frojeciions of Shadows when the Sun's Rays copte on the Front of the Figure. Having already explained the theory of this in what has now been advanced, it remains only to give an example or two to illuftratc it. . Example I. Fig. 45. Plate XXVI. When the Shadow falls on the Ground. In Fig. 45, A is a prifm whofe fliadow is projedled by the fun as above propofed, h is the vanifhing point of the fliadow, V of the fide of the cube, and S of the rays. Therefore from the angles i, 2, 3, draw lines to h\ and from 4, 5, 6, at the top, correfponding with thefe, draw lines to S, cutting at % c, b \ I from ( 341 ) from b draw a line to <r, and fi-om c to 9, which, when filled up, will complete the fhadow. Example II. Fig. 46. Plate XXVI. 'ur- When the Shadow falls at the fame Time on upright^ oblique ^ and horizontal Plajies. !0 "J This figure having the moft necefTary lines for reprefent- ing the two houfes, as well as for finding the lliadow of one houfe falling upon the other, may be confidered as an example both of perfpe6live and of fliadow. And as the lines for both are here joined together in one view, it will Hiew their relation, and the necefTary dependence they have on each other ; Avhich, it is prefumed, will contribute more to the learner's advantage, than if many examples of fhadowing had been added without regard to the perfpecftive lines. The horizon and ground line being drawn, fix the center of the pi6lure as ufual ; from which raife a perpendicular as to d. Make d the diiiance of the picture, and, according to the obliquity fuitable for the front of the houfe, draw a line to V, for one vanifhing point; next draw V d, and from d draw a line to V, at right angles with V d\ becaufe the end and front of the houfe are originally at right angles to each other. Make v M equal to vd^ and whatever angle the pitch of the roof makes, produce ( 342 ) produce a line from M equal to that angle, continued till it cut a line perpendicular to v, as at V ; then is V the vanifliing point for the fide of the roof of both houfes, and a line from V to V will be the vanifliing point of the plane which the roof is in, and H will be the vanifliing point of fliadows lying in the faid plane ; and producing V V at pleafure, and meeting it in o at Fig. 44, by a parallel from S, o will be the vanifliing point of the fun's rays on that plane. Extend the compalTes from V to «y, and place it below the horizon, and that point will ferve for the other fide of both roofs. The houfes being completed in their outlines, according to thefe vanifliing points, proceed to fliade them upon a fuppofition that the light comes on in the front of the picflure, and in a dire(ftion from the left hand pa- rallel to the dotted line dh. Therefore the point b will be the vanifliing point of the fhadows falling upon the ground plane, and producing b perpendicular to the vanifliing line V V, H will be the vanifliing point as aforefaid. The place of the fun S is fixed very losv, not as a precedent, but that it might throw the fliadow of the firft houfe on the fecond, affording an occa- fion of fliewing the nature of fuch fliadows. From o; the pitch of the roof on the gable-end, draw a line to S ; and from a draw a fine to b^ which will cut the front of the other houfe at o; from o raife a perpendicular, cutting the line drawn from ^ to i? in ^ ; from e diredl a line to V, the va- nifliing ( 343 ) nifliing point for the fronts of each houfe, which gives the fliadovv for the roof. From the tops of each chimney draw lines to S, and obferve that the fliadovv of the firft chimney falls partlj^ on the roof, becaufe the ray drawn to S cuts the roof, and that ray muft be cut again, by drawing a line from the top of the perpendicular fliadow o ^ to H, the vanifliing point of fuch fliadows as fall on the roof, and from the top of the fha- dow on the roof diredt a line to o, in Fig. 44, which gives the complete fliado w of the chimney. Laftly, from ^, at the bottom of the fecond houfe, draw a line to b ; and cut that line by two others, one from the top of the chimney, and another from the pitch of the roof, as before; from thefe interfedlions draw lines to V, the vanifliing point of the houfe, and the fliadows will be finiflied.. Of Shadows when the Sun is not fuppofed to Jhine, or thofe pro^ duced by common Light, After what has been faid on fliadows produced by the fim, it will not be requifite to fay much on this head. It will, however, admit of a few remarks. And firfl:, fuppofe an objedt ^, b^ c. Fig. 47, placed to the light, and confider the parallel lines as rays of common 4ight falling on it ; for common light directs its courfe to ob- jeds. l( 344 ) }e£ts in this manner. Now it is evident, therefore, that the fide or plane a m ill have moft of the light, becaufe the rays fall nearly perpendicular on it, which confeqnently excludes all' fliadow ; but the plane or fide ^ receives the faid rays obliquely,- and in proportion thereto occafions a fliadow, becaufe the light partly mifles the furface. The plane e is totally in fliadow, be- ' caufe the ray r cannot touch that furface. Secondly, in fliadows of this kind the contraft of light and fliade is not fo fi:rong as when the fun's rays fall on obje<fls ; the light is not fo glaring, nor the fliadows fo black. The out- lines of fuch fliadows ought not to be ftrongly defined, but faint, and fometimes indifl:in£l, efpecially when the light is fup- " pofed to come from different apertures. Laflly, fuch obje<51:s as are fuppofed to be viewed in a room , have their upper parts lighteil ; but the lighted parts will bear a tint, and fometimes confiderable, fo that there will not be much oppofition of light andfhade in their different furfaces. It is requifite to confider the natural colours of obje6ls, in order to fix the tone and true fcale of light fuitable to them -. The lighteil: part of an objecfl that is of itfelf black,' would be * This is alfo necefiary \yhen the fun is fuppofed to iliine. a fliade ( 345 ) a fhade to one that is white, and therefore, in producing a fha- dow to any thing black or blue, it will require all the force and ftrength of the Indian ink. The other colours, as green and yellow, &c. will alfo require a due degree of light and Ihade to diflinguilli them by. Mr. Kirby confiders the colours receding from white to black in the following order: / e. yellow after white, then green, red, blue, and black, fucceffively. It is difficult, how- ever, to diftinguifli fome of thefe by the effedl of Indian ink, yet it is evident fomething may be done towards it. Thus : the cube W is fuppofed to be white, Y yellow, G green, R red, B blue, and BL black-^'-. Of the Proportion of Tints fuited to ObjeHs at different DijJances in the fame PiBure. See a View, Plate XXVI. It is evident, from the nature of perfpedive in general, that not only the proper dimenfions of objeds, but alfo the de- gree of tint, is eflential in making them appear at different dif- This is not the order of the fimple colours, according to Sir Ifaac Newton's theory of their origin. His theory informs us, that when the rays of light are feparated by the re- fradion of a prifm, the firft will be red, then orange, yellow, green, blue, indigo, and violet, fucceffively. See his Optics, Book I. Prop. 6. According to this, white is not a fimple colour, but a compound or mixture of all that are fimple, and black a total privation of every colour. X X tances. ( 346 ) tanccs. For, as in iineai^ perfpeclive, objcifls are viewed under a fnialler angle in proportion as they are at a diftance, fo in the aerial part every tint and Ihadow gradually weakens as the obje6t is iituated at a diitance from the front of the picture. The reafon of this is obvious, when it is admitted that we are made to fee obje6ts by innumerable beams of light iffuing from them to the eye. It is eafy then to conceive, that when thefe beams or rays of light have to make their way through the air from diftant parts of the horizon to the eye, they muft greatly weaken before their arrival to it, and therefore fuch diftant objeds muft appear lefs diftindl and more dim in proportion to that diftance. Hence, in a pi(5ture, as in the view given in Plate XXVI. objedls on the fore ground are not only larger, but they are more made out, more diftindl, and ftrongly marked. Their lights are brighter, and their fliades are darker, than thofe on the back ground. This will, perhaps, be more eafily underftood by the following obfervations on the view. The tree on the left is neareft to the eye of the fpeilator, and is therefore moft made out ; its leaves are feen in clufters, and its fliade is ftrong. The firft tree on the right, being further back, is lefs dif- tinft in its parts, and rather fainter in its ftiadows ; and fo of the reft in proportion to their diftance. With ( 347 ) With refpeil to the honfes, we fee the fecond weaker in its parts, and its fhadow, partly on the water and on the ground, fainter than that of the firft. The laft houfe being at a vaft diftance, appears as one mafs without diftinftion of parts ; and thus objedls diminifh off till they and the horizon on which they Hand mix with the fky. Of the reflected Images of ObjeHs on Water, To afcertain the reflected images of objects on water is ex- ceeding eafy, and very elTential to fome pi6tures. It is a law in catoptrics ••'-, that the angle of refic6tion is always equal to the angle of incidence t. The angle of incidence and refledlion may be thus under- ftood and diftinguifhed. The inclined pofl, and its fhadow on the water, form an angle with each other; and at the bottom of the poll, where the line of refledlion on the water and the line * Catoptrics, from KottCivlpov, katoptron, a mirror or looking-glafs. Catoptrics teach the fcience of reflex vifion, and optics that of direft vifion, though in tlie general and ex- lenfive meaning of the term optics, " from cnrhy-ai, optomai, I fee," it includes in it «' whatever relates to fight, or the doftrine of vifion ;" and therefore mull imply dioptrics alfo, which teaches the properties of refracted vifion ; that is, when rays of light pafs through one medium into another, as air and water. t See fecond axiom of Sir Ifaac Newton's Optics. X X 2 of ( 348 ) of incident rays from the poll meet, that point is termed the point of incidence ; and if from the top of the poll a perpendi- cular be let fall, it will form a triangle ; and if that triangle be bifeaed, that is, by drawing a parallel line from the point of incidence b, cutting the perpendicular at c, then the angle c, «, b, is the angle of incidence, and c, d, b, the angle of refle<flion, •which are equal. Therefore if an objed: be perpendicular to the horizon, its refleaed image on water will alfo be perpendi- cular, but in an inverted pofition to the objedl which refle<5ls the image. And whatever angle of obliquity any objedl makes Avith the ground, the fame will be its refledlion to the furface of the water. The refleclions of images on water are the fame as thofe in a plain mirror. The furface of the mirror or looking-glafs is the plane of reflexion ; and it is evident, that in whatever pofi- tion any objev5l is prefented to it, the fame will be that of its re- fledion on the faid plane. If a rod, &c. be placed perpendicular to the mirror, its refleiled image will be perpendicular to it alfo. And if one end of it touch the glafs, its image will alfo appear to touch the furface of it ; or if it is withdrawn, its image will appear equally removed from the refledling plane. This expe- riment is within the reach of every one, and will be fufficient to convince any of the truth of the above propofition. Example ( 349 ) Example I. See the View, Plate XXVI. If, therefore, the reflexion of the indined poft be wanted, let fall a perpendicular at pleafure, and cut that per- pendicular by a line drawn from the bottom of the poft in- clining to the faid perpendicular in an angle equal to the ob- jedl, and it will give the length and inclination of the refleaed image. And obferve, that the length of the refleaion on the water will be in proportion to the diftance of the objea from it; confequently if the poft were removed a little fur- ther from the edge of the water, we fliould lofe its refleaion entirely. Example II. If it be required to find the refleaion of any of the trees fuppofed to ftand nearly perpendicular, let fall a perpendicular from the bottom of it, and take the whole height of the tree and place it downwards from the bottom of it, then take the length of the trunk and do likewife, which will give the reflec- tion as required. Laftly, ( 350 ) Laftly, it is manifeft from thefe principles, that if any obje<5l be floating in the water, fuch as a piece of timber or a Ihip, that its refle6ted image will be equal in length to the objedt itfelf, and the depth of the refle£tion below the fur- face of the water will be equal to the height of the obje(5t above it. END OP THE SECOND PART. THE THE CABINET-MAKER AND UPHOLSTERER'S D R A W I N G-B O O K. PART III. CONTAINING A DESCRIPTION OF THE SEVERAL PIECES OF FURNITURE. I. OF THE USE AND STYLE OF FINISHING EACH PIECE. 2. GENERAL REMARKS ON THE MANUFAC- TURING PART OF SUCH PIECES AS MAY REQUIRE IT. 3. AN EXPLANATION OF THE PERSPECTIVE LINES WHERE THEY ARE INTRODUCED. TO WHICH IS ADDED, A CORRECT AND QUICK METHOD OF CONTRACTING AND ENLARGING COR- NICES OR OTHER MOULDINGS OF ANY GIVEN PATTERN. INTRODUCTION. The defign of this Part of the Book is intended to exhibit the prefent tafte of furniture, and at the fame time to give the workman fome afliftance in the manufadiiring part of it. I am fenfible, however, that feveral perfons who have al- ready encouraged the work, will not want any help of this 3 nature ; ( r,^ ) nature ; but it is prefumed many will who are not much con- verfant in the bufinefs, and who have had no opportunity of feeing good pieces of furniture executed. For the advantage of fuch, it is hoped that the experienced workman will exercife candour and patience in reading the in- ftru6tions intended, not for himfelf, but for thofe now men- tioned. There are few but what may, with propriety, refleft on their own paft ignorance, even in things which afterwards be- come exceeding fimple and eafy by a little practice and experi- ence. Such a refledlion ought, therefore, to promote both candour and good nature in the minds of proficients, when they read the documents neceffary to young beginners. And yet, I hope, it may be faid, without arrogance, that it is probable the experienced workman may derive fome information from the fubfequent remarks, when it is confidered that they are made not merely from the knowledge and experience I have myfelf of the bulinefs, but from that of other good workmen. In converfing with cabinet-makers, I find no one individual equally experienced in every job of work. There are certain pieces made in one fhop which are not manufadlured in an- other, on which account the beft of workmen are fometimes Itrangers ^::-^z •( 353 ) ftrangers to particular pieces of furniture. For this reafon X '\ have made it my biifinefs to apply to the beft workmen in dif- ferent fhops, to obtain their affiftance in the explanation of fuch v ?-=^ pieces as they have been mofi: acquainted with. And, in gene- "* ral, my requeft has been complied with, from the generous ''''■ motive of making the book as generally ufeful as poffible. The methods therefore propofed, and the remarks made, may be depended on by thofe who have not yet had an oppor- ^ ^ tunity of feeing the different pieces executed. - ■ '■ , This is an attempt which has not yet been made in any %' i •book of cabinet defigns, except a very few flight hints; and, '~ v though it muft be acknowledged by every impartial mind as highly ufeful, and even in fome cafes abfolutely neceffary, yet I am apprehenfive it will not meet Vvdth the approbation of thofe who wifh to hoard up their own knowledge to them- felves, left any Ihould fliare in the advantage arifnig from it. In fome inftances it may be neceffary for a man to keep know- . ledge to himfelf, as his own property, and upon which his bread may depend; but I do not fee any impropriety in perfons of the fame branch informing each other, hi trades where their arts depend on fecrets, it is right for men to keep them from ftrangers ; but the art of cabinet-making depends fo much on practice, and requires fo many tools, that a ftranger cannot Y Y fteal ( 354 )' 'ileal it. But in every branch there are found men who love to- keep their inferiors of the fame profeffion in ignorance, that themfelves may have an opportunity of triumphing over them.. From fuch I expert no praife, but the reverfe. Their pride will not fufFer them to encourage any work which tends to make others as wife as themfelves ; and therefore it is their fixed refolution to defpife and pour contempt upon every at- tempt of this kind, in proportion as it is likely to fucceed. But thofe I will leave to themfelves as unwortliy of notice, who only live to love themfelves, but not to alTift others.. Here I would beg leave to obferve, that it is natural for every man under a heavy burden to pour out his complaint to the firft fympathizing friend he meets with^ If the reader be one of thefe, I will pour out mine, by informing him of the difficult taik: I have had to pleafe all, and to fuit the various motives which different perfons have for encouraging a pubU- cation like this. I find fome have expedted fuch defigns as never were fetn, heard of, nor conceived in the imagination of man ; whilft others have wanted them to fuit a broker's fliop, to fave them the trouble of borrowing a bafon-ftand to fhew to a cuftomer. Some have expetfted it to furnifli a country wareroom, to avoid the expence of making up a good bureau, and double cheft of drawers, ( 35S ) drawers, with canted corners, &c. and though it is difficult to conceive how thefe different quaUties could be united in a book of fo fmall a compafs, yet, according to fome reports, the broker himfelf may find his account in it, and the country mafler will not be altogether difappointed ; whillf others fay many of the defigns are rather calculated to fliew what may be done, than to exhibit what is or has been done in the trade. According to this, the defigns turn out to be on a more general plan than what I intended them, and anfwer, beyond my expe6tation, the above various defcriptions of fubfcribers. However, to be ferious, it was my firft plan, and has been my aim thtough the whole, to make the book in general as per- manently ufeful as I could, and to unite with ufefulnefs the tafte of the times ; but I could never expetSt to pleafe all in fo narrow a compafs : for to do this, it would be necefTary to com- pofe an entire book for each clafs of fubfcribers, and after all there would be fomething wanting ftill. Y y a A DE- ^ SA^ ) & DESCRIPTION OF. THE SEVERAL PIECES OF FURNITURE. Oft/je UniverfalTabk. Plate XXV. of the Cabinet Defigns,. The ufe. of this piece is both to anfwer the purpole of. a: breakfaft and a dining-table. When-both the leaves are flipped under the bed, it will then ferve as a breakfafl-table ; when one leaf is out, as in this view, it will. accommodate, five perfons as a dining-table; and if both are out, it will admit of eight, being near feven feet .long, and thr^e feet fix inches in width. . The drawer is divided into frx boxes at each fide, as in the plan, and are found ufeful for different forts of tea and fugar, and fometimes for notes, or the like. In tliis drawer is. a flider lined with green cloth to write on. The flryle of finifliing them is plain and fimple, with ftraight tapered legs, focket caftors,.. and an aftragal round the frame. . Of the maniifa&uring Part: This table fhould be made of particularly good and wtll- feafoned mahogany, as. a great deal depends upon its not being liable jVT'ij: /^/./. /•/af,' 'js. J£ U / >/////. r/,v//'- J/ 'ar/c' z <■ t:^-^^ ^^ ^ t juUdiii Wf ■iiH ^imw^ J. *' Ji lll"'ll"""""l"""'l"''i'. t;^i^4i€/'i'nf yMe.' ^>\iAe i>^m* jtJ^^rj J^ /■M.-r.,tm J^/. /'ii/>/i/JMhis[/ii\.li-r liim-r^fM- (? Terry ^y<if la j;^i. ( 357 ) liable to cafl. In the beft kind of thefe tables the tops are- framed and pannelled ; the bed into two pannels, and the flaps each into one, with a white firing round each pannel to hide the joint. The framing is three inches broad, and mitered at the corners ; and the pannels are fometimes glued up in three thickneffes, the middle piece being laid with the grain acrofs,. and the other two lengthways of the pannel, to prevent its warping. The pannels are, however, often put in of folid Huff, without this kind of gluing. Wlien the pannels are tongued into the framing, and the miters are fitted to, the tops Ihould ftand to flirink as much as poffible before they are glued for good. There are different methods of fecuring the miters of the framing. Some make iimply a flraight miter, which they can flioot with a plane; after which they put a couple of wooden pins in. Others, again, having fitted the miters to by a plane, they flip in a tenon. But the Itrongeft method is to mortice and tenon the miters to- gether, having a fquare joint at the under,, and a miter joint at the upper fide. This method, however, is the moft tedious of the tliree, and where the price will not allow of much time,, the above methods are more ready,, and, if managed with care, are fufiiciently flrong. In gluing the miters, it will be proper,, firfl, to glue on the outfide of each miter a piece of deal in the fliape of a wedge, which will take a hand-fcrew, fo that when thef ( 358 ) they are putting together, the glue may be brought out, and the miters made clofe. The frame, as fliewn in the plan, is made exactly fquare, either of faulty mahogany, or of wainfcot veneered. In making this frame a box is formed at each end, about three inches in width, containing two Aiders apiece, which run paft each other in the faid box, as fliewn in the plan. In the bottom of each box are put two pieces, with plough grooves in them, and raking contrary to each other. In the line N O, on thofe raking pieces the Aiders run, and are flopped from coming too far out by a pin fixed in the under edge of the Aider; which pin runs in the plough grooves already mentioned, denoted in the plan by a dark line. The raking line of the Aiders is found by taking the width of the Aap, as from S to M, and making the line in- cline in that width equal to the thicknefs of the flap. This may be eafdy underftood, by placing a rule from the outer point M of the flap, to S the inner point, whidh then will be parallel to the raking line. The Aiding pieces being in a right line their whole length at the under edge, of courfe their upper edge muft be bevelled off, fo that when they are drawn' fully out, they may be even, and in an exacSt line with the top of the frame. The frame and tops being thus prepared, they are con- nected together by an iron fcrew and nut, as at A, which is about ( 359 ) about the fub fiance of a bed-fcrew. This fcrew is jointed into a plate, which plate is let into the under fide of the bed, level with it ; though I have defcribed it at A with its thicknefs out, merely that the plate might be Ihewn. At B the bed A is repre- fented on the frame, and the iron fcrew paffing through the rail of the table, is confined to its place by the nut, which is let ipto the under edge of the rail by a center-bit. And obferve, in making this center-bit hole for the nut, it muft be funk deeper than its. thicknefs, that the bed may have liberty to rife a little, and {o give place to the flaps when they are wanted to be puflied in. It mufl be noticed alfo, from the plan of the frame, that there is a middle piece, about five inches, broad, and of equal thicknefs with the- flaps, fcrewed down to the frame with four fcrews at each end. This middle piece an- fwers three purpofes ; it fecures the frame, flops the flaps., when they are puflied in, and prevents the Aiding pieces from tilting. Before the bed is finally fixed to its place, there mufl be four pieces of green cloth let into the under, fide of it, to pre- vent the flaps from rubbing as they Aide under. Upon the edges of the flaps a hollow is worked all round, leaving a quarter of an inch fquare, for no other purpofe than to take off the clumfy appearance of the two thicknefTes when the flaps are * under ( 36o ) under the bed. At the under fide of the flaps mud be goged out finger-holes, to draw them out by. The drawer is next to be confidered, which is fometimes made with two fronts, and to draw out both ways, as in the plan. On each front of the drawer is a lock, for the conveni- ence of fecuring it at either end ; for in cafe one flap be drawn out, then the drawer can be locked or pulled out at the contrary front, without the trouble of pufhing the flap in to come at the drawer. The covers of each box before mentioned, may have an oval of dark wood, and the alphabet cut out of ivory or v/hite wood let into them, as in the plan; or they may be white ovals and black letters ; the ufc of which is to diftinguifli the contents of each box. Laftly, the Aider to write on is made exaiflly half the infide length of the drawer ; fo that when it is puflied home to either front, there is immediate accefs to fix of the boxes. And here I would obferve that fometimes the flaps of thefe tables have round corners, but they do not anfwer the bed {o well when they are in. And, to fave expence, the tops have been found to anfwer the purpofe in folid wood, without being framed. ( 36i ) framed. When they are made in this manner, particular regard fhoukl be had to placing the heart fide of the wood outward, which naturally draws round of itfelf, and may therefore be expelled to keep true, notwithftanding its unfavourable fitu- ation. N. B. The heart fide of a board is eafily known by plan- ing the end, and obferving the circular traces of the grain,, which always tend outwards. "the Perfpe&lve Lines, explained. In making defigns in perfpe6live, the firft thing to: be at- tended to is the fcale of feet and inches, by which t(i proportion: the different pat ts to each other, to determine the height of the horizon, and the diilance of the picture. Having made the fcale, take from it about five feet fix for the height of the horizon at H L. On this line place the point of fight, fo as to give the moll favourable view of the defign, as at s. Next lay on the dillance, which is here out of the plate, and being equal to the fpace s a. agrees to the rule for choofing a diftance contained in page 28 [. Draw ab perpendicular to the ground line, and from a draw a line to the point of fight s. Z z Next ( 3^2 ) Next confider how much the top proje6ls over the frame, and as much as this is, lay it from a towards ^, as the firft Une Ihews, which is dire<Sted to the point of diftance. Where this cuts the aforefaid Hne drawn to j-, raife a perpendicular anfwer- 'ing to a b. From b lay on the fpace b d^ for the depth of the framing; and from d draw a line as before to s\ and from where the line cuts the fecond perpendicular, draw a parallel for the under edge of the framing. On a parallel line from b^ lay on the dimeniions of the bed and flap; and from thefe draw lines to j, as the defign fliews. Now, as the bed of the table is fquare, nothing more is wanted to find its apparent width than to draw a line from o to the diftance which cuts at the oppofite angle ; and through this angle draw r t parallel, which com- pletes the out-line of the top. To find the place of the drawer and the boxes in it, pro- ceed thus. — On the ground line make a e equal to the whole fpace, from the drawer in the plan to the projedtion of the middle piece acrofs the frame. Alfo make e b the whole length of the drawer, and ,?/the diviilons for the boxes. From each of which draw lines to the diftance, cutting at 1,2,3,4; from which draw parallels to 7, 6, 5, 8. Again, from 7 raife a per- pendicular, and make k b^ on k m^ equal to the height of the drawer; from b draw a line to s\ and from ;;/, the height of the covers of each box, do the fame. Laftly, from 6, 5, &c. raife 1^>«=~: fei 'j ^ 6 #= ■ !-/■• /// /. T. Sftrr.ihft iff/fn . Pii/>li/^tefi (?s t/uAi'C Jiix'cU.fy (r lerry—Ifecj !j<fi . C 363 ) raife perpendiculars, which will cut b s in the place for th& boxes, and at n for the height of the covers. How every other thing is done, muft be obvious from infpedtion. Of the Sideboard Tables, Plate XXYl. and XXIX. and of Tables of this Kind in general. The fideboard in Plate XXVI. has a brafs rod to it, which is ufed to fet large diflies againft, and to fupport a couple of candle or lamp branches in the middle, which, when lighted, give a very brilliant effe6l to the lilver ware. The branches are each of them fixed in one focket, which Aides up and down on the fame rod to any height, and fixed any where by turning a fcrew. Thefe rods have fometimes returns at each end of the fideboard; and fometimes they are made ftraight, the whole length of the fideboard, and have a narrow Ihelf in the middle, made of full half-inch mahogany, for the purpofe of fetting fmaller dilhes on, and fometimes fmall lilver ware. The right-hand drawer, as in common, contains the cel- leret, which is often made to draw out feparate from the reft. It is partitioned and lined with lead, to hold nine or ten wine bottles, as in Plate XXiX. Z z 2 The ( 364 ) The drawer on the left is generally plain, but fometimes divided into two ; the back divifion being lined with baize to hold plates, having a cover hinged to enclofe the whole. The front divifion is lined with lead, fo that it may hold water to wafh glaffes; which may be made to take out, or have a plug- hole to let off the dirty water. This left-hand drawer is, how- ever, fometimes made very fliort, to give place to a pot-cup- board behind, which opens by a door at the end of the fide- board. This door is made to hide itfclf in the end rail as much as poflible, both for look and fecrecy. For which reafon a turn- buckle is not ufed, but a thumb-fpring, v/hich catches at the bottom of the door, and has a communication through the rail, fo that by a touch of the finger the door flies open, owing to the refiftance of a common fpring fixed to the rabbet which the door falls againft, as is denoted by the figure A. F is for the finger, B is the brafs plate let into the rail, L is the lever, p is the fpring that prefTes the lever upwards, and c is the end of it which catches the under edge of the door as it pafTes over it and llrikes into a plate with a hole in it, and s is the fpring fcrew^ed to the rabbet ■^^ hich throws the door out when F is puflied upwards. But the reader muft here obferve, that the fliape of this lideboard will not admit of a cupboard of this fort in the end raiJ. ( 365 ) rail. Thofe which are fquare at the ends, and only a little ihaped in front, are fitteft for this purpofe. In large circular fideboards, the left-hand drawer has fome- times been fitted up as a plate-warmer, having a rack in the middle to ftick the plates in, and lined with llrong tin all round, and on the underlide of the fideboard top, to prevent the heat from injuring it. In this cafe the bottom of the drawer is made partly open, under which is fixed a fmall narrow drawer, to contain a heater, which gives warmth to the plates the fame as in a pedeflal. In fpacious dining-rooms the fideboards are often made without drawers of any fort, having fimply a rail a little orna- mented, and pedeftals with vafes at each end, which produce a grand efFe6t. One pedel1:al is ufed as a plate- warmer, and is lined with tin ; the other as a pot-cupboard, and fometimes it contains a celleret for wine. The vafes are ufed for water for the ufe of the butler, and fometimes as knife-cafes. They are fome- times made of copper japanned, but generally of mahogany^ There are other fideboards for fmall dining-rooms, made without either drawers or pedeftals ; but have generally a wine- cooper to ftand under them, hooped with brafs, partitioned and lined with lead, for wine bottles, the fame as the above-men- tioned celleret drawers. The ( 366 ) The fideboard in Plate XXIX. fliews two patterns, one at each end. That on the left is intended to have four marble flielves at each end, inclofed by two backs, and open in front, Thefe flielves are ufed in grand fideboards to place the fmall iilver ware on. The pattern on the right is intended to have legs turned the whole length, or rounded as far as the framing and turned below it, with carved leaves and flutes. The divifion beyond the celleret-drawer is meant for a pot-cupboard. It is not ufual to make fideboards hollow in front, but in fome circumftances it is evident that advantages will arife from it. If a fideboard be required nine or ten feet long, as in fome noblemen's houfes, and if the breadth of it be in proportion to the length, it will not be eafy for a butler to reach acrofs it. I therefore think, in this cafe, a hollow front would obviate the difficulty, and at the fame time have a very good effe6t, by- taking off part of the appearance of the great length of fuch a fideboard. Beiides, if the fideboard be near the entering door of the dining-room, the hollow front will fometimes fecure the butler from the joflles of the other fervants. Of ( 367 ) Of the Perfpe&ive Lines. Having drawn the plan and adjufled the height of the ho- rizon by the fcale, as was mentioned in the univerfal table, re- prefent a parallelogram a, b, c, d, equal to the length and breLdth of the table; and from every part of the plan draw lines up to the ground line, and from the ground line direft thefe to the point of fight. Take from the plan the fpace M N, and place it from 1 to 2 ; and from ^ diredt a line to the point of diftance, cut- ting a point next to;;; from which point draw a parallel for the place of the front legs. In like manner take the other dimen- fions from the plan to find every other correfpondent point in the reprefentation. To find the reprefentation of the hollow and round fronts, confult the treatife on perfpedive in pages 294 and 295> together with the lines here fliewn as hints, and it is prefum- ed that the learner will not be at any lofs in drawing fuch a table. Of the Book-cafe Doors. Plate XXVlI. and XXIX. In the execution of thefe doors, the candid and ingenious workman may exercife his judgment, both by varying fome parts of the figures, and taking other parts entirely away, when the door is thought to have too much work. ^ No. I, C 368 ) No. I, in Plate XXVII. might do for a plain door, if the- ornament and fquare part in the middle were taken away. No. 1 might alfo have the fquare in the middle taken away,, and look very well. No. 4 may have the upright and horizontal bars away, and No. 5 the fmall fquares ; and at each angle of the hexagon the ftraight bar might be carried through to the frame. Witli refpecH: to No. 6, it may be ufeful to fay fomething of the method of making it, as well as of fome of thofe in Plate XXIX. The firft thing to be done, is to draw, on a board, an oval of the full length and breadth of the door. Then take half the oval on the fliort diameter and glue on blocks of deal at a little diftance from each other, to form a caul ; then, on the fliort diameter, glue on a couple of blocks, one to flop the ends of the veneer with at tlie time of gluing, and the other, being bevelled off, ferves to force the joints of the veneer clofe, and to keep all fall till fufficiently dry. Obferve, the half oval is formed by the blocks of the fize of the aftragal, and not the r ibbet ; there- fore confider how broad a j^icce of veneer will make the aftra- gals for one door, or for half a door. For a whole door, which takes -vrm. />/. Dt^OR.-S for ]3D0I\ CASES ri<7/c 7 L .T/ n-; .1 'T? ilillllllllllllMIIIMilllllllllllllliill!llllilllllllllllllllH!illllM s m r\ "^.-i r\'o /'.I'/iefyiivn de/ - J^blifh'd oj- the Act duvets by (rTerry- .May^.ijpt. Bofifiw feufyy . /-'. /J/./. DnoR.-i for _Boo.l\l'ASi:S PM,' 'jc) T'y ■■fflHillilllllMliiBllllllinillH^ dy:6. yi.'y.,/ /'///•///h,/ ilJ- f!„- , li-f ,/il>;tr fy G.'/ii "ti ( 369 ) takes eight quarter ovals, it will require the veneer to be inch and quarter broad, allowing for the thicknefs of a fafli faw to cut them off with. Veneers of this breadth may, by proper management, be glued quite clofe; and if the veneer be ftraight baited, and all of one kind, no joint will appear in the aftragal. Two half ovals thus glued up, will make aftragals for a pair of doors, which, after they are taken out of the cauls and cleaned off a little, may be glued one upon the other, and then glued on a board, to hold them faft for working the aftragals on the edge; which may eafily be done, by forming a neat aftragal in a piece of foft fteel, and fixing it in a notched piece of wood, and then work it as a gage ; but before you work it, run on a gage for the thicknefs of the aftragal; and after you have worked the aftragal, cut it off with a fafli faw, by turning the board on which the fweep-pieces are glued on an edge; then having fawn one aftragal off", plane the edge of your ftuff* again, and proceed as before. For gluing up the rabbet part, it muft be obferved, that a piece of dry veneer, equal to the thicknefs of the rabbet, muft be forced tight into the caul ; and then proceed as before in gluing two thicknefles of veneer for the rabbet part, which will leave fufficient hiding for the glafs, on fuppofition that the aftragal was glued in five. 3 A The ( 370 ) The door being framed quite fquare, without any mould- ing at the inner edge, proceed to put in the rabbet pieces. Put, firft, an entire half oval, and fcrew this to the inner edge of the door, and level with it; then jump up the other half oval to it, and fcrew it as before; which completes the center oval. Next, fix the fquare part, having been before mitered round a block, and keyed together; after which, half-lap the other quarter ovals into the entire oval where they crofs each other, and into the fquare part, liping it into the angle of the door; put in the horizontal bars for the leaves to reft on; glue on the aftragals, firft on the entire oval, tying it with pack- thread, to keep it on ; then the ftraight one on the edge of the framing, fitting it to the oval ; lailily, miter the aftragal on the fquare part, and every other particular will follow of courfe. With refpedt to the doors in Plate XXIX. all of them may be made nearly on the fame principles, at leaft the rabbet parts muft ; but the aftragals in No. i, being all of them portions of circles, fliould be cut out of folic! wood, and glued on a deal board and fent to the turner's. The fame may be faid of No. 5, which, in the vafe part, may have a piece of filvered glafs. The center in No. 2, is intended to have a print or painting in it. The fweeps, in No. 6, fliould be cut out of the folid, and worked by a tool. As to fixing any part of the ornaments in- troduced in thefe doors; this is eafily done, by preparing a very A-/. /^/. J' j'ArraJtn Sri Fu^it/^d €if CA^:/ict dir€cCr. fy & Tern : Dec "24 '*'jjai ILSarl^- uufy r\ ( 371 ) very ftrong gum, which will hold on glafs almofl: as ftrong as glue on wood. Of the Secret ajy and Book-cafe. Plate XXVIII. The ufe of this piece is to hold books in the upper part, and in the lower it contains a writing-drawer and clothes-prefs flielves. The defign is intended to be executed in fatin-wood, and the ornaments japanned. It may, however, be done in mahogany ; and in place of the ornaments in the friezes, flutes may be fubftituted. The pediment is fimply a fegment of a circle, and it may be cut in the form of a fan, with leaves in the center. The vafes may be omitted to reduce the work : but if they are introduced, the pedeftal on which the center vafe refts is merely a piece of thin wood, with a necking and bafe moulding mitered round, and planted on the pediment. The pilafters on the book-cafe doors are planted on the frame, and the door hinged as ufual. The top of the pilafters are made to imitate the Ionic capital. Of the Perfpe&ive Lines. G R is the ground line, and H L the horizontal line, or height of the eye. Lay on the original heights of the book. 3 A 2 cafe, ( 37^ ) cafe, as at gyb,i,J, k, ?c;r. and draw a perpendicular line at the angle of the piece, as at A ; to which diredt parallel lines as fliewn. On the ground line lay a, or two feet, for the breadth of the end ; and from 1/ a diredt lines to the diftance, which is. here out of the plate, cutting the vifuals at fl'*?; from e raife a perpendicular, which will determine the front of the book-cafe, provided it be only a foot deep. The perpendicular B is necef- fary, in order to find the perfpedlive heights of the book-cafe, as fliewn in the figure. Of the Library Table. Plate XXX. This piece is intended for a gentleman to write on, or to ftand or fit to read at, having defk-drawers at each end, and is generally employed in fi:udies or library-rooms. It has already been executed for the Duke of York, excepting the defk-draw- ers, which are here added as an improvement. The ftyle of finiflimg it ought to be in the medium of that ■which may be termed plain or grand, as neither fuits their fituation. Mahogany is the moft fuitable. wood, and the orna- ments fhould be carved or inlaid, what little there is; japanned ornaments are not fuitable, as thefe tables frequently meet with a little harfli ufage» The C 373 ) The rtrength, folidity, and effe<£l of brafs mouldings are very fuitable to fuch a defign, when ex pence is no objedt. For inftance, the pilafters might be a httle funk, or pannelled out and brafs beads mitered round in a margin, and foUd flutes of the fame metal kt in. The aftragal which feparates the upper and lower parts might be of brafs ; and likewife the edge of the top, together with the patera in the upper pannel, as fliewn on the left hand. The top is lined with leather or green cloth, and the whole refts and is moved on caftors hid by the plinth. Of the mamifa&ur'mg Part'. The top fliould be framed in inch and quarter wainfcot, in the figure of a long hexagon, which bed fuits the fhape of the oval. 1 he pannels, which are tongued in, fhould be of at leafl: three quarters hard mahogany, about nine inches fquare, and the ftiles three and an half broad. The top being thus framed of very dry wood, it fliould be planed over, and fl:and for fome time at a moderate diftance from a fire, after which it may be glued together, and when hardened it ought to be planed over again, and remain in that ftate till the lower part is finiflred. If thefe methods are not purfued, the pannels will flirink, and their joints will draw down the leather or cloth, fo that the figure ( 374 ) figure of the framed top will appear, efpecially when it is lined with leather. Next, it muft be confidered how to glue on the mahogany on the framing, fo as to make the furbafe moulding appear of folid wood. Firft, plough the four fliort fides of the hexagon, and then tongue in fuitable mahogany lengthways, meeting in a ftraight joint in the center of the top; and, laftly, after the tongiung is dry, glue in ftraight joint pieces on the two long iides of the hexagon, and when dry, the top will be prepared for cutting to its elliptic fliape. The manner of framing the upper and lower parts of the carcafe muft be learned from the plan. The upper part, framed in an entire oval, contains the defk-draw^ers ; and, if thought neceflary, two fliort ones may be obtained over the fide niches. The cupboard part is framed in two, each of which has a niche at the end, and one-third of the fide niches; for the niches are all of them divided into three pannels, and the middle pannels of the fide ones ferve as doors, by which an open paf- fage is gained through the table. There are four cujjboards in the whole, divided in the manner fpecified by the dotted lines in the ( 375 ) the plan, one or two of which may be fitted up in a neft of fmall drawers and letter-holes. The plinth is framed entire of itfelf, and the bafe-moulding Hands up a little to receive the whole and hide the joint. In putting on the bafe-moulding there are two or three methods which I would otter as the belt I know of. The frame being made fo thick as to take the projection of the bafe, it muft then be rabbeted out of the folid to receive it. This being done, proceed to glue the bafe in three or four thicknefTes, con- fining them to their place by hand-fcrews, or other devices of that nature ; but obferve to let the bafe project further out than the deal plinth, that it may receive the mahogany veneer which is to be glued on lengthways to hide the deal. After the whole is glued faft to its place, the veneer on the plinth and the bafe muft be cleaned off level with each other* The convex parts of the bafe-moulding may be worked with hollows and rounds; and after thefe are finifhed, the niches Ihould be worked down to them, by a tool made on purpofe. Another method of gluing the bafe-moulding is as follows : — Prepare the inch deal, and make cauls to fit the end and fide niches of the plinth ; after which take ftraight baited three- I eighths ( 376 ) eighths Spanifli wood, and work the hollow part of the bafe fe- parate from the torus; then, from quarter ftufF of the fame kind, cut off flips for the torus ; heat the caul well, and both wet and heat the flips, which will then eafily bend. When the hollow part is well tempered, and alfo the torus, begin at one end, and by a thin chip run glue in between them ; and as you go on drive in nails about every inch, having between the nails and the moulding a thin Hip of wainfcot well heated. Obferve to let the moulding pafs beyond the caul at each end, that a pack-ftring may be tied to keep it to its place when it is taken out. The torus may then be worked before it is glued on the plinth- A third method is, to make the plinth itfelf the caul, and firft work the hollows, and foak them in water a whole night. Next morning take a hand-iron and heat it well, and over the curved fide of which bend the hollow as near as may be to the fweep. Having already a flop fcrewed on the plinth, jump one end of the moulding to it, and glue as you go on ; at the fame time fixing fmall hand-fcrews to draw it to, or brads may be put through the fquare part to affift in this bufinefs, if necef- fary, for thefe will be covered by the torus. After the hollow is fufficiently dry, the torus being worked oiF and well foaked, and bent round the iron as above, it will glue to the hollow without the fmalleft difficulty, by firll: jumping it againrt the flop ( 377 ) flop before mentioned ; and after it is brought pretty near, take another flop and fcrew it againft the end of the torus, which will draw it down without further trouble. Thefe two methods are founded on experiment ; for, at my requeft, it was per- formed by fome cabinet-makers to my full fatisfa6tion ; there- fore, fliould either of thefe methods fail in the hands of any, it mull; be owing to fome defedl in the management. Of the Perfpeciive Lines. Draw firft a plan of the whole, and make G R the ground line, and H L the horizon. From the plan draw perpendicular lines from every part to G R, as fliewn in the Plate ; make s the center, and lay on the diftance, which is here out of the plate. From each j^erpendicular line drawn to G R draw lines to j- then reprefent a parallelogram both at top and bottom, in which the ellipfis maybe infcribed; and draw the diagonal correfpond- ing with that fliewn in the plan, which will cut the vifual drawn from the faid diagonal in the plan, finding a point to guide the ellipfis. For other particulars relative to the repre- fentation of an ellipfis, fee page 294, and Plate XXI ; for the re- prefentation of the niche, fee page 295 ; and for the deik-drawer, fee page 231, Prob. 4. 3B Of ( 378 ) Of the Kidney Library Table. Plate LVIir. This piece is termed a kidney-table, on account of its re- femblance to that inteftine part of animals fo called. Its ufe, however, is the fame as that already defcribed. The drawers which appear in the delign arc all real, and are ftrung and crofs-banded, with the grain of the mahogany laid up and down. The pilafters are pannelled or crofs-banded, and the feet below turned. The view of it below fliews the ends pannelled, and the back may be fo too, or it may be plain. With refpedt to the manufaduring part, I need not fay any thing after what has been faid on the other, except to explain the reading defk which Aides out, as fliewn below. Obferve, B is the profile of the frame which Aides out, in the Q(\<gQ of which there is a groove fliewn by the black ftroke, and a tongue is put into the edge of the well part to fait it. F is the delk part which rifes by a horfe; and A is a part of that, which rifes at the fame time to flop the book ; ^ is a tumbler-hinge let in flufli with the top, and hid by the cloth or leather ; <r is a com- mon but:-hi?ige let in the edge of F, and upon the frame B ; fo that when F falls to B, A does alfo. The length of the table is four feet, its width two, and its height thirty-two inches. Of N'^j.^l.,^ ^y JTinA^KY 7:uiLJ':. X-^-^. rS/ifriifl-n .Jlf . IiM>Jh/«J-/irJrfi/tr^ti'. /r ^ Terry ^ rrt. /f. f^rj/i iS,r,...f? TMutith'ii ./'■/' Xirjy .^'■"V ' Utif^its Ihf Aet tirttl' ftf> T :ii' tloi t-v u Terrv M ( 379 ) Of the Sofa Bed. Plate XXXI. The frames of thefe beds are fometimes painted in orna- ments to fiiit the furniture. But ^vhen the furniture is of rich filk, they are done in white and gold, and the ornaments carved. The tablets may have each a fertoon of flowers or foliage, and the cornice cut out in leaves and gilt has a good effetft. The drapery under the cornice is of the French kind ; it is fringed all round, ^nd laps on to each other like unto waves. The va- lance ferves as a ground, and is alfo fringed. The rofes which tuck up the curtains are formed by lilk cord, &c. on the wall, to fuit the hangings; and obferve, that the center rofe contains a brafs hook and foeket, which will unhook, fo that the cur- tains will come forward and entirely enclofe the whole bed. The fofa part is fometimes made without any back, in the manner of a couch. It muft alfo be obferved, that the befl: kinds of thefe beds have behind what the vipholfterers call a fluting, which is done by a flight frame of wood faftened to the wall, on which is ftrained, in ftraight puckers, fome of the fame fluff of which the curtains are made. The left plate fliews the plan of the tefter, and the manner of fixing the rods, which are made in two parts to pafs each 3 B 2 other, ( 38o ) other, fo that the curtains may come clofe to each other in the center. The tefter rods fcrew foft in front, and hook pail each other behind. The manner of fixing the tefter up is by an iron bracket at each end; one arm of the bracket fcrews to the under- iide of the tefter, and the other againft the wall, by driving in plugs for that purpofe. Of the Ferfpe&ive Lines. The left plate fliews thefe lines, and the right fliews the fcales of proportion. Thefe beds feldom exceed twelve feet in height, including the feather at top. Thek length is feven feet, and width about five. The perfpedive lines are drawn by a contra6led diftance, being only one third of the whole. The front of the fofa is merely a geometrical elevation. For the apparent width of it take five feet from the fmall fcale, which is termed one third of the real fcale of feet and inches ; place this meafurement from 14 to ^, and draw a line to J, cutting at 15 ; a^b^ d, are for the tablets at each end; and at /is laid on the full meafurement of the back tablet, from which lines are drawn to s the center, which ALi^OA^w ny,:D Ao T. JA^rabn dtiin , /. Barlct^Jat^. /"li/f/z/hr^/ /:ir fhfjij-^ a/r€t^.iy T.Shrra/p7iiFeh-4.ljti% ( 38r ) v/!iicli cuts the back of the fofa at the line i^, i6, and deter- mines its length. The back tablet being the higheft, lay on the additional height from to, and draw a line to s, cutting a per- pendicular at ii; from which draw a parallel as fliewn. The line drawn through /j is to find the front of the dome, which comes forward rather fliort of half of the breadth of the fofa. The line 4 is the back of the doiae, 5 is the center line, and 3 is its front ; 7 Ihews the- height of the under fide of it, 8 of the top of the cornice, and 9 the top of the dome ; the reft muft be ua- derftood by obfervation. Oftbe Alcove Bed. Plate XL. The term alcove, in buildings, means a part of a room fe- parated off from the reft by columns and arches correfponding, in which is placed a bed : fo that it is not the particular form of the bed which gives rife to this name, but the place in- which it Hands. The learned inform us, that the word alcove is from the Arabic elcauf^ which means a cabinet or fleeping-placc- This defign is reprefented ftandmg on a plinth, covered with carpet, and having a border round it fuppofed to be on the floor of the room. The ft:eps are introduced to fliew that beds of this fort are raifed high, and require fomething to ftep on before they can be got into. The fteps are generally covered with ( 382 ) with carpet, and framed in mahogany. Both this, the fofa, and French ftate hed, require fteps. The dome of this bed is fixed in the fame manner as the other ; but the rofes to which the curtains are tucked up are different. This is made of tin, and covered with the fluff of the bed, and unbuckles to take in the curtains behind the rofe. Upon the fluting, as before men- tioned, is fixed a drapery in this, as fhewn in the defign ; and fometimes in the arch of the alcove a drapery is introduced. Of the Summer-Bed in two Coujpartmejits. Plate XLI. These beds are intended for a nobleman or gentleman and his lady to lleep in feparately in hot weather. Some beds for this purpofe have been made entirely in one, except the bed- clothing being confined in two drawers, running on rollers,: capable of being drawn out on each fide by fervants, in order to. make them. But the preference of this defign for the purpofe^ mufl be obvious to every one in two or three particulars. Firfl, the pafTage up the middle, which is about twenty- two inches in width, gives room for the circulation of air, and Hkewife affords an eafy accefs to the fervants when they make the beds. Secondly. >•"/'. /»/./. FU:4/. kA-^^ \^// /// ////^'rji^^^^r/-/ /m ^/?Jef^ (/■u?///a//////f/^/.i LKKi'-ristih^jkj.Xjkj^ik' '' 7eet iimi Z/tc?tfS S/iera/tit .2^ el . Sm-UwS.;Jj, Jhiili/hei/ au' t-he Ai-t Jirfetj' ir e. Terry. — . Junt ZO. I-^a^. ( 383 ) Secondty, the paflTage gives opportunity for curtains to en- clofe each compartment, if neceffary, on account of any fudden change of weather. Thirdly, it makes the whole confiderably more ornamental, uniform, and light. The firft idea of this bed was communicated to me by Mr. Thompfon, groom of the houfliold furniture to the Duke of York, which, I prefume, is now improved, as it appears in this defign. The manufadturing part may eafily be underftood from the defign by any workman; I fliall, however, point out a few par- ticulars. The arch which fprings from the ionic columns fhould be glued up in thicknefs round a caul, and an architrave put on each fide afterwards. The arch fliould be tenoned into the co- lumns, with iron plates fcrewed on, fo that it may be taken off when the bed is required to come down, hi this arch a drapery is fixed, with a taflTel in the center, and a vafe above. The head-board is framed all in one length, and the two inner fides of the bed tenoned into the head-rail, and fcrewed. The tefter is made in one, in which there are two domes, one over each compartment. It may, however, be made without domes, but Diot with fo good effedt. In the middle of the tefter, perpendi- I- cular C 384 ) cular to the fides of the paflage, are fixed two rods, for the cur- tains above mentioned. Thefe rods are hid by valances, and between the valances is formed a pannel, by fewing on va- riegated margins to fuit the reft of the upholftery work. The ornamented margins, and the oval with crefts in the center of the counterpanes, may all be printed to any pattern, at a manu- fadlory which has been lately eftabliflied for fnch purpofes. The fcale fiiews the fizes which applies to every part of the end of the bed, it being merely a geometrical elevation. Of the French State-Bed. Plate XLV. Beds of this kind have been introduced of late with great fuccefs ill England. The ftyle of finifiiing them, with the management of the domes, is already defcribed in general terms, in page 113, 8cc. 1 fliall, therefore, omit it here, and proceed to give fome hints relative to the manufac^turing part. The dome is fupported with iron rods of about an inch diameter, curved regularly down to each pillar, where they are fixed with a firong fcrew and nut. Thefe iron rods are covered and entirely hid by a valance, which comes in a regular fweep, and meets in a point at A :h'Fs>:^iN(i:e STATI*-. 'l3KB'(«LI'C;)FFXTSl'irTTATKrJ T'(> TME nCTUl^E V] ui JTi'Amt/^i c^U < /S/ *at Me-^U AnxGr Je^ "iff *X^2 /f -/" . i^^-mlan. 7\m/Au-€it^^^ /Oi/^ 1 ( 385 ) at the vafcs on the pillars, as the defign lliews. Behind this va- lance, which continues all round, the drapery is drawn up by- pulleys, and tied up by a filken cord and taffels at the head of the pillars. The head-boards of thefe beds are framed and ftuiTed, and covered to fuit the hangings, and the frame is white and gold, if the pillars and cornice are. The bed-frame is fome- times ornamented, and has drapery valances below. Obferve, that grooves are made in the pillars to receive the head-boards, and fcrewed at the top, by which means the whole is kept firm, and is ealily taken to pieces. Square bolfters are now often introduced, with margins of various colours Hitched all round. The counterpane has alfo thefe margins; they are alfo fringed at bottom, and have fometimes a drapery tied up in cords and taffels on the fide. Of the Perfpe&ive Lines, This defign is in an oblique fituation, fo termed becaufe none of its ends or fides are parallel to the picture. I have- here taken the neareft angle of the bed for the center of the pic- ture, from which raife a perpendicular as from feven on the fcale line. Confider next the height of the horizon, which fliould be about five feet fix, taken from the fcale you draw the 3 C bed ( 386 ) bed by. On the perpendicular line now mentioned lay on the diftance of the picture from the horizontal line. Then deter- mine the pofition of one fide of the bed, by drawing a line from the angle E to V ; from V draw a line to the diftance here out of the plate, on the aforefaid perpendicular ; from the diftance draw a line TU at right angles with this, which produced cuts the horizon, and finds the vanifliing point for the ends of the bed ; confequently V is the vanilhing point for the fides of the bed. From 7 to A is feven feet, the length 'f the fide; and from 7 to N is the width of the bed. From N A draw lines to D D, the dividing centers, or meafuring points, found as in Problem VI. Method 2. page 237, which will cut the vifuals for the apparent length and width of the bed. A perpendicular from 5 is the center of the end of the bed ; S is the original height of the dome, from which a line is directed to the right hand vanifliing point, cutting at d; a line from ^ finds the cen- ter of the dome, and V the top of the pine-apple; c a give the height of the cornice ; the diagonals i, 3, 2, 4, find the center of the dome, by railing a perpendicular from their interfection. Every other thing will follow of courfe to him who has previ- oufly ftudied the rules given; without which, it would be im- pofhble to make ever}'' particular underftood here. Of ^' < ■ K 0" % ^ (^ h 8 K^ "^ -te8 I- : Ml •Si 3k. t ^ V 1^ s5 ^■^ ^ ^^ '^ ^:^JJUVi; i JUJ T. J r)=f ]ff ep¥-fcfe t J ' I [ ^ SM^ J'XL^Ji/ ^ ^p=?!rrTT!?? ^ ■\'1 S ^ ( 387 ) Of the Drawing-Room Chairs. Plates XXXII, XXXIV. These chairs are finiflied in white and gold, or the orna- ments may be japanned; but the French finifli them in maho- gany, with gilt mouldings. The figures in the tablets above the front rails are on French printed filk or fatin, fewed on to the fluffing, with borders round them. The feat and back are of the fame kind, as is the ornamented tablet at the top of the left-hand chair. The top, rail is pannelled out, and a fmall gold bead mitered round, and the printed filk is pafted on. Chairs of this kind have an elBfea which far exceeds any conception we can have of them from an uncoloured engraving, or even of a coloured one. The perfpeaive lines in the left chair may ferve as hints ; but I need not explain them, fince I have fully done this in Plate XXIV. and XXVI. The parlour chairs in Plate XXXIII. and XXXVI. need no explanation, as every one muft eafily fee how they are to be finifhed. 3C2 0/ ( 388 ) Of the Sofa. Plate XXXV. These are done in white and gold, or japanned. The loofe cufhions at the back are generally made to fill the whole length, which would have taken four; but I could not make the defign fo ftriking with four, becaufe they would not have been dif- tinguillied from the back of the fofa by a common obferver. Thefe cufliions ferve at times for bolfters, being placed againft the arms to loll againft. The feat is fluffed up in front about three inches high above the rail, denoted by the figure of the fprig running longways ; all above that is a fquab, which may be taken off occafionally. If the top rail be thought to have too much work, it can be finiflied in a flraight rail, as the defign fliews. Of the Lady's Writing "table. Plate XXXVII. The convenience of this table is, that a lady, when writing at it, may both receive the benefit of the fire, and have her face fcreened from its fcorching heat. The ftyle of finifliing them is neat, and rather elegant. They are frequently made of fatin-wood, crofs-banded, japan- ned, and the top lined with green leather. The '::s ,5^ ^ ^ V ^ J ( 389 ) The maniifacSluring part is a little perplexing to a ftranger, and therefore I have been particular in fliewing as much as I well could on the plate. Obferve, that in the fide-boxes the ink-drawer is on the right, and the pen-drawer on the left. Thefe both fly out of themfelves, by the force of a common fpring, when the knob on which the candle-branch is fixed is preffed. Figure A is the fpring which is let in under the candle-branch ; C is a lever which is prelTed to B, the end of the drawers, by a fpring rifing from D ; N is a part of the candle-branch, and e is the knob juft mentioned, which is capable of being prelTed down ; there- fore, if P be fcrewed into E by preifing ^, C rifes and relieves B, which immediately ftarts out, by a common fpring fixed on the infide of the boxes. Obferve a patera in the center of the back amidft the orna- ment. This patera communicates to a fpring of precifely the fame kind as A; which fpring keeps down the fcreen when the weights are up: and by touching the faid patera, which has a knob in its center like e^ the fpring is relieved, and the weights of courfe fend up the fcreen, being fomewhat affifted by a fpring at the bottom, which may be feen in the defign. Figure T fliews the lead weight, how the pulleys are fixed, and the manner of framing the fcreen before it is covered with fluff. I The ( 390 ) The workman will obferve, that a thin piece of mahogany Aides out in a groove, to afford accefs to the weights, and afterwards enclofe them. There is a drawer under the top, which extends the whole of the fpace between the legs. The fcale fliews the length of the table, b its height, a the depth of the drawer, b c the depth of the fide-boxes, and e d the height of the fwell of the fcreen part ; the width of the table is twenty inches » 0/ the tripod Fire-Screens. Plate XXXVIII. Screens of this kind are termed tripod*, becaufe they have three feet or legs. The middle fcreen may be finiflied in white and gold, or japanned; and the other two of mahogany, or japanned. The rods of thefe fcreens are all fuppofed to have a hole through them, and a pulley let in near the top on which the line paffes, * Tripod, of T'fEif, treh three ; and itohw, podien, a foot. Anciently the word tripod xifed to be applied to a kind of facred three-footed ftool, on wliich the heathen priefts were feated to receive and deliver their oracles r from which we may learn how time alters words. and •"-/ z*'-^ JViYIlFE, CASES. />/^i^ y »<vli. /n< Aty. TS/irnf.t' ./?./ 2U : oj- fLA€t. Jt'rerAf /y ^ Terry Mv, 2y. n^SL . f^l^rry Sa/^l ( 39^ ) and a weight being enclofcd in the taffel, the fcreerl is balanced to any height. The rods are often made fquare, which indeed beft fuits thofe which have pulleys, while thofe that are made round have only rings and fprings. Such fcreens as have very fine prints, or worked fatin, commonly have a glafs before them, hi which cafe a frame is made, with a rabbet to receive the glafs, and another to receive the ftraining frame, to prevent it from breaking the glafs; and to enclofe the ftraining frame a bead is mitered round. Of the Knife-cafes and Ladfs TravelHng-Box. Plate XXXIX. Little need be faid refpeding thefe. It is only wanted to be obferved, that the corner pilafters of the left-hand cafe has fmall flutes of white holly or other coloured wood let in, and the middle pilafters have very narrow crofs-bands all round, with the pannels japanned in fmall flowers. The top is fome- times japanned, and fometimes has only an inlaid patera. The half columns of the right-hand cafe are fometimes fluted out, and fometimes the flutes are let in. The feet may be turned and twifted, which will have a good eifedl. A5 ( 392 ) As thefe cafes are not made in regular cabinet fhops, it may be of fervice to mention where they arc executed in the heft tafte, by one who makes it his main bufincfs ; /. e. John Lane, No. 44, St. Martin's-le-grand, London. The Lady's travelhng-box in the fame plate, is intended to- accommodate her in her travels with conveniences for writing, dreffing, and working. The front is divided into the appear- ance of fix fmall drawers; the upper three fliam, and the under real. The ^vriting-drawer takes up tN'^o of thefe fronts in length, and contains an ink-drawer, and a top hinged to the front, lined with green cloth. The top being hinged at front, by pulhing in the drawer, it will rife to any pitch. The other drawer on the left, which only takes up one front, holds a kind of windlafs or roller, for the purpofe of fixing and wmding up lace as it is worked. The middle vacuity, which holds the fciffors and other articles of that nature, takes out, which gives acccfs to a convenience below it for holding fmall things. The boxes on each lide hold powder, pomatum, fcent-bottles, rings, Sec. The dreffing-glafs, which is here reprefented out of the box,, fits into the vacuity above the fciiTor-cafe. 0/ C 393; ) Of the Corner Bafon-Stands. Plate XLII. The right-hand bafqn-ftand contains a cupboard amV a real drawer below it; by the top folding" down the bafon is inclofed and hid when it is not in vife. The left-hand top is fixed to the fide of the bafon-ftand by a rule-joint, the fame as the flap of a Pembroke table; but inilead of iron the hinges are made of brafs. The right-hand top is hinged to the other by common butt-hinges, by which means it will fold againft the other, and both may be turned down together. When the tops are in their place, there then appears a rule-joint on both fides. The front edges of the tops are hollowed and beaded, which hang a little over, fo that the fingers may get hold to raife them up. Short ' tenons are put to the under edge of the right-hand top, to keep it in its place on the end of the lower part. The bafon ftand on the left has a rim round the top, and a tambour door to inclofe the whole of the upper part, in which is a fmall ciftern. The lower. part has a flielf in the middle, on which fl:ands a veilel to receive the dirty water conveyed by a pipe from the bafon. Thefe fort are made large, and the bafon being brought clofe to the froiit, gives plenty of room. The , advantage of this kind of bafon-fiand is, that they may iland in a 3 D genteel ( 394 ) genteel room without giving offence to the eye, their appearance being fomewhat hke a cabinet. Of the Dejigns in Plate XLIII. The drawer in the wa(h-hand ftand is lined with lead, into which the bafon is emptied. The upper part, which contains the ciftern, takes off occafionally. Below the drawer is a cup- board. Obferve, that in the defign the drawer back is fuppofed to be behind the bafon ; but before the drawer is wholly taken away, the bafon muft be taken out. Of the Pot-Cupboard. These are ufed in genteel bed-rooms, and are fometimes finiflied in fatin-wood, and in a Ityle a little elevated above their ufe. The two drawers below the cupboard are real. The par- titions may be crofs-banded, and a ftring round the corners of the drawer. Thefe feet are turned, but fometimes they are made fquare. Sometimes there are folding doors to the cup- board part, and fometimes a curtain of green filk, fixed on a brafs wire at top and bottom ; but in this defign a tambour door is ufed, as preferable. The upper cupboard contains flielves, and is intended to keep medicines to be taken in the night, or to hold other little articles which fervants are not permitted to overlook. Of .\:..,i./'/.i /'/ 1-^ e / '/ '/.i// ' //t^r //</ ' ^/f/y/f/. y.fii,-,,,/,.,, ,/,./ Ji/M.i/u/ /■,/ /r.Irrri/. ir/zZ^. V/ef^-. ( 395 ) Of^be Ladfs Secretary. These are fometimes finifhed in black rofe-wood and tulip crofs-banding, together with brafs mouldings, which produce a fine eifeft. The upper Ihelf is intended to be marble, fup- ported with brafs pillars, and a brafs ornamented rim round the top. The lower part may be fitted up in drawers on one fide, and the other with a flielf to hold a lady's hat, or the like. Of the Screen-Table. This table is intended for a lady to write or work at near the fire ; the fcreen part behind fecuring her face from its in- juries. There is a drawer below the Aider, and the Aider is lined with green cloth. The back feet are grooved out for the fcreen to Aide in ; in each of which grooves is fixed a fpring to balance the fcreen by. The top is firll: crofs-banded all round ; then a border is put on, fo broad as to fall exa6lly where the joint of the fcreen will be in the top. Beyond that again is put a narrower crofs-banding. When the fcreen is down the top appears uniform, without any joint, at leaft not fo as to be ofFenfive to the eye. The ftraining 3 D 2 frame ( 396 ) frame of the fcreen is made of thin wainfcot, and framed in four pannels. When the faid frame is covered in the manner of any other fcreen, Hips are got out and grooved and mitered round, and a part of the top which rifes up with the fcreen is glued on to the flip, and as of courfe the top will project over behind, fo it affords hold for the hand to raife the fcreen by. Off/je two tables, Plate XJJV. The left-hand table is to write and read at. The top is lined ^vith leather or green cloth, and crofs-banded. To Itop the book there are two brafs plates let in, with key-holes ; and in the moulding, which is to flop the book, are two pins, with heads and flioulders, by which the moulding is effe.^tu^Ily fecured. < • The right-hand table is meant to write at only. The top part takes off from the under part, which, having a bead let in at the back -and ends of the top, prevents the top part from moving out of its place. This table being made for the conve- nience of moving from one room to another, there is a handle fixed on to tlie upper flielf, as the di-awing fliews. In the drawer is a flider to write on, and on the right-hand of it ink, fand, and pens. The fizes are fliewn by the fcales. Of r ^^ I? I ^^' 3'.''/-'. /^/-'. r \ ^f/f/zfli . ^'■/(■(.i/zu/ . ^f//'/r Pliiri-4C> H Uu o (0 ^ e. o o o li (^ W^M. ^111 i~T~ r -i T~-r-T [ />/•*' X Inches T. Sheraton dfl .PaHish./ US th- A.! '/nrrts /r ff 7>^r h'lh'ry.Snilp ( 397 ) Of the Lady's Dr effing "table. Plate XLVI. The ftyle of finifhing thefe tables is neat. They are often made of fatin-wood, and banded ; but fometimes they are made of mahogany. The fize of this table, which is here three feet, fliould be increafed in its length near fix inches when thefe folding fide-glaffes are introduced. The reafon of this is, that a lad}^ may have more room to lit between them to drefs. It fliould, in this cafe, be made about two inches widen But, ob- ferve, the llze here given is that which is ufed when only the rifing back-glafs is introduced ; and this has been the common w ay of finifliing them. Thefe fide-glaffes are an addition of my own, which I take to be an improvement; judging that, when they are finifiied in this manner, they will anfwer the end of a Rudd's table, at a lefs expence. The glafs behind rifes up like that of a fliaving-ftand. Thofe on the fide, fold down paft each other, being hinged to a iViding ftretcher, which is capable of being puflied backward or forward. If the right-hand glafs be pufiied to the back it will then fold down, and the other keeping its place will do the fame. A and B, in the plan, fliew thefe glaffes in their place ; e is the back-glafs, and / is the top, which is hinged to a piece of ( 398 ) of wood, which runs in a groove at each end, fo that when the top is drawn fully up, it will fall down on the frame. The other folding top on each fide have each of them a fmall tenon near the front, as may be feen at the edge of the left-hand one. Thefe tenons being let into the middle part, are the means of fecuring each fide-top, when they are folded down, and the middle part is put down upon them, fo that the lock in the middle fecures the three tops. The drawer on the right is the depth of two fronts, as is eafily feen ; the ufe of which is to put caps in. The left-hand fronts are in two real drawers, for the purpofe of laying fmall things in. The cupboard in the knee- hole has its front reeded in the hollow part to imitate tambour, and the circular door in the center is veneered and quartered. This cupboard will take a lady's hat as they wear them now. The other drefTing conveniences are obvious in the plan. Of the PerfpeHive Lines. These I only confider as hints or memorandums to fuch as have already gone through the regular trcatife on the fubjecft. an\% the width of the table; and a line fi'om a to r/, the diftance, cuts the vifual n s in b^ which gives the apparent width at that diftance. The front of the table is fuppofed to be in the pic- ture, and therefore every meafurement is purely geometrical; that is, they are taken from the fcale. From r to o is the width 7 of ( 399 ) of the top, except the flip behind. Therefore by drawing a perpendicular at />, and directing a line from o to j-, the center, it will cut at /), and give the height of the top, fuppofing it to be raifed quite up, ready for turning down. Of the Cylinder Dejk and Book-cafe. Plate XL VII. The ufe of this piece is plain, both from the title and de- fign. The flyle of finifhing them is fomewhat elegant, being made of fatin-wood, crofs-banded, and varniflied. This defign fliews green lilk fluting behind the glafs, and drapery put on at top before the fluting is tacked to, which has a good look when properly managed. The fquare figure of the door is much in fafliion now. The ornament in the diamond part is meant to be carved and gilt, laid on to fome fort of filk ground. The rim round the top is intended to be brafs ; it may, however, be ^Jone in wood. Of the manufa&uring Part, The manufacSturing part of this piece is a little intricate to a ftranger, for which reafon it will require as particular a defcription as I can give to make it tolerably well under- llood. Firll-, C 400 ) Firft, obferve the flider is communicated with the cylinder by an iron trammel, as I,fo that when the former comes forward, the latter rifes up and fliews the nell: of the fmall drawers and letter holes, as appears in the defign. When, therefore, the Hider is puflied home even with the front, the cylinder is brought clofe to it at the fame time In this ftate the lock of the long drawer under the flider fccures both the drawer itfelf and alfo the flider at the fame time, in the following manner: — D is the long drawer under the flider, P the partition above it, and S is the flider ; C is a fpring-bolt let into the partition. When, therefore, the drawer lock-bolt is out, as it rifes it drives C, the fpring-bolt, into the flider ; and when the drawer is unlocked, then C falls down to its place in the partition, and the flider can be pulled out. The trammel I, ^s a piece of iron near a quarter thick, and inch and quarter broad, with grooves cut through, as fliewn at I. S, in the profile, is the flider; and ^^, 12, //, the cy- linder. The trammel T is fixed to the cylinder at h by a fcrew, not drove tight up, but fo as the trammel will pafs round eafy. Again, at the flider S a fcrew is put through the groove in the trammel, which works on the neck of the fcrew, and its head keeps the trammel in its place ; fo that it muft be obferved, that the grooves or flits in the iron trammel are not much above a quarter of an inch in width. When tlie flider is puflied in about half way, the trammel will be at w, and its end will be below the flider, as the plate fliews; but v/hen the flider is home C 40I ) home to its place, the trammel will be at T and g. The center piece with four holes is a fquare plate of iron, having a center- pin which works in the upper llit of the trammel. It is let into the end of the cylinder, and fixed with four fcrews. To find the place of this center, lay the trammel upon the end, as T b, in the pofition that it will be in when the Aider is out, and, with a pencil, mark the infide of the flits in the trammel. Again, place the trammel on the end as it will be when the flider is in, as at T^, and do as before ; and where thefe pencil marks interfe6l each other will be the place of the center-plate. The figures i, 2,3,4, fhew the place of the fmall drawers. The triangular dotted lines with three holes, is a piece of thin wood fcrewed on to the end, to which is fixed the neft of fmall drawers, forming a vacuity for the trammel to work in. F is a three-eighth piece veneered and crofs- banded, and cut behind to give room for the trammel. This piece both keeps the Ihder to its place, and hides the tram- mel. The next thing to be obferved is, that the lower frame, containing two heights of drawers, is put together feparate from the upper part, which takes the cylinder. The ends of the cylinder part are tenoned with the flip tenons into the lower frame and ghied. The fliaded part at A fhews the rail cut out to let the trammel work. The back is framed in two pannels, and the back legs are rabbetted out to let the back framing come down to the lower drawer. The flider is framed of ma- hogany, with a broad rail at each end about nine inches, and' 3 E one. ( 402 ) one at the front about three and an half. In the inlide of the framing a rabbet is cut to receive a thin bottom. The bottom being fixed in, a flip is put at each end to receive the horfe which fupports the deflc part. The ink and pen drawers at each end of the Aider have a fmall moulding mitered round them to keep them faft, without their being glued on. Obferve, there is a £ham drawer-front faftened on to the Aider, which of courfe goes in with it, and which contains the depth of thefc ink and pen drawers, fo that they are not required to be taken out when the Aider goes in. The cylinder is jointed to its fweep in narrow Alps of ftraight-baited hard mahogany, and afterwards veneered. If the veneer be of a pUable kind it may be laid with a hammer, by firft flirinking and tempering the veneer well, which muft not be by water, but thin glue. If the veneer be very crofs and unpliable, as many curls of mahogany are, it is in vain to at- tempt the hammer. A caul in this cafe is the fureft and beft method, though it be attended with confiderably more trouble than the hammer. To prepare for laying it with a caul, pro- ceed as follows.— Take five or fix pieces of three-inch deal, and fweep them to fit the infide of the cylinder. Fix thefe upon a board anfwerable to the length of the cylinder. Then have as many cauls for the outfide of the cylinder, which may be made out of the fame pieces as thofe for the infide. Take then quarter mahogany for a caul to cover the whole veneer, and heat it well. Put the caul fcrews acrofs the bench, and Aip in the 8 board j\rp2. />/.2. fiA/,S. a/^^/ie^tj^ i9lw^ J'<i? a cr auA' ^z^ C^c^ £t>Ai>le d&s^h/UT^. 7- Br-€^/Jt <y/' Uwe/" ^ay^ "'•/i/h .^ /7.f fAe .'ii-t dir^-ij' hy it 7h-rv . Ano fl /" ( 403 ) board with the round cauls fcrewed to it ; and proceed, in every other particular, as the nature of the thing will neceffarily didtate. Of the Perfpe&ive Lines, GR is the ground line, and H L the horizon ; s the center, and d the diftance of the picture. A B, on the ground line, is the breadth of the ends ; from which a line is drawn to d^ cut- ting the vifual B j, for the perfpedlive breadth of the end. O is the height of the lower part, and the upper part being level with the horizon, appears in one line, and therefore flievv^s no breadth at the top. Of the Cabinet. Plate XLVIII. The ufeof. this piece is. to accommodate a lady with con- veniences for writing, reading, and holding her trinkets, and other articles of that kind. The ftyle of finifhing them iselegant, being often richly japanned, and veneered with the fineft fatin-wood. The manufacturing part is not very difficult, but will ad- mit of the following remarks. — The middle drawer over the 3 E 2 knee- ( 404 ) knee-hole has a Aider to write on, and thofe on each fide are plain. The doors under them are hung with pin-hinges, and in the infide there is one flielf in each. The cupboard within the knee-hole is fitted up in finall drawers, and fometimes only a fiielf. The pilafters or half columns are put on after the car- cafe is made. The corner ones are planed fquare firft, and then rabbetted out to receive the angle of the carcafe, and afteru'ards tlcal is glued in a flight manner into the rabbet, that it may be eafily taken out after the column is turned. The center door of the upper part is fquare at the top, opening under the aftragal which finiflies the cove part. The pilafters are on the door frame, and the drapery is formed and fewed to the filk, and both are tacked into a rabbet together. Behind the filk door are Aiding flielves for fmall books. The wings are fitted up as Aiewn in the defign on the right, or with more fmall drawers, having only two or three letter holes at the top. Of the Perfpe&ive Lines. G R is the ground line, H L the horizon, and s d only half the full diftance of the pidlure ; wherefore ^ ^ is only half the original meafurement of the ends of the cabinet. A perpendi- cular from e determines the front of the upper part, and all thofe .v.'V./. /j/ H Jlnf^ ^. ^lihrmfe^ft. •/'/ /'///•//.r//,/ /7x //^ .-/-A (^rVV^r/j, 4)' Ir Terrv. _ ^ -'V^>-. J, <7^2 . &Ter-f'y.t?*^//f (405) thofe vifuals drawn to s are obvious in themfelves. The per- pendicular lines cc, at the cove, fhew the centers for drawing it. The right-hand door opens more than fquare, confe- quently it is oblique to the pi6lure; and being oblique, the top and bottom of it tend to fome vanifliing point out of the center of the pi6lure, as is denoted by the lines n n, s s. Thefe two, if produced, would meet in a point on the horizon, and that point is termed the vanifliing point of all lines parallel to the top and bottom of the door. The door turning on its hinges de- fcribes a femicircle, as is Ihewn; and, confequently, every open- ing of the door muft come within the circumference of that femicircle. " Oftbe Ladfs Cabinet Brejfmg-I'abk. Plate XLIX. This table contains every requifite for a lady to drefs at. The ftyle of finifhing them is neat and fomewhat elegant. With refpe£l to the manufacturing part, and what it con- tains, thefe may be learned from the defign itfelf, which here fhews the parts entirely laid open. I fhall therefore only men- tion two or three particulars. When the wafhing-drawer is in, a Aider which is above it may be drawn out to write on occa- lionally. The ink. and fand are in the right-hand drawer under the ( 406 ) the center dreffing-glafs. Behind the drapery, which is tacked to a rabbet, and fringed or gimped, to cover the nails, is a flielf, on which may fland any veffel to receive the dirty water. Above the drapery are tambour cupboards, one at each end, and one in the center under the drawer. Above the tambour at each end are real drawers, w'hich are fitted up to hold every article neceffary in dreffing. The drawers in the cabinet part are in- tended to hold all the ornaments of drefs, as rings, drops. See. Behind the center glafs is drapery ; it may be real to fuit that below, or it may only be painted in imitation of it. The glafs fwings to any pofition, on center pins fixed on the flielf above the candle-branches. The fide-glaflTcs fold in behind the doors, and the doors themfelves, when fliut, appear folid, with ovals in the pannels, and ornamented to fuit the other p^rts, Ob- ferve, the whole plan of the top is not in the plate, it being re- quired to be two feet over. The perfpedlive lines fliewn at the circular end, are as fol- lows. — When the plan is made, divide the curve into parts, as Ihewn ; and from thefe divifions on the ground line, draw lines to the center s. Then turn up the ordinates to the ground line ; and from the points where they cut on that line, draw lines to the diftance, as fhewn, which will cut the vifuals at 6, 7, 8, 9, and fo on, finding points to diredt the curve by. Of -\T/3. />/. a. rlatr.iP. ^ H ^ ^Q^..l£j^j 9:UL/ .w V//x////./^. %//fy ' /ett and Iru^ej ' MUM TSA-^^B^H l}itl J*tiiii/heii /zr the Jcf tiirecU M ^ 7^'rrt' April Jr. m^s A « Baf/'-if j:-n/^. ( 407 ) Of the Lady's Cabinet and Writing-Table. Plate L. This table is intended for writing on, and to hold a few fmall books in the back of the upper part. Within the door at each end, under the domes, are formed fmall cabinets of drawers, &c. The front of the upper part, which inclofes the neft of drawers and letter holes, ilides in under the top, and when drawn fufficiently out falls down in the curve fg^ and locks into the folding top. The method of hinging this front is thus : — Suppofe BD to fhew it up, as it is in the defign, ready for pufliing home. Then obferve, D ^^ is a (lip which runs in a groove cut at each end. The front B is rabbetted out, and alfo the flip D. Thefe are hinged together, and are both of one thicknefs, fo that when B is drawn out, the flip having a tenon at d^ flops it from com- ing entirely out. The other figure fliews the front when it is let down, which cannot fail of making it underflood. The dotted curve line oP fliews that the imder fide of the top muft be hollowed out fo that the angle of the falling front may clear itfelf as it turns. Obferve, ( 4o8 ) Obferve, the writing part folds over like a card-table, and when it is open, is fupported by the drawer in the frame. Every other part muft be plain to the workman. N. B. Upon the fame principles the top of the dreffing- table, Plate XLVI. is managed. . Of the Drapery. Plate LI. Little can be faid of this, as every part explains itfelf, as reprefented in the drawing. It is, however, necelTary to ob- ferve, that the French ftrapping and taffels in the right-hand defign is no part of the cornice, as fome cabinet-makers have already miftaken it to be. It is the upholfterer's work, and is fewed on within the valance or ground of the drapery. Thefe curtains are drawn on French rods. When the cords are drawn the curtains meet in the center at the fame time, but are no way raifed from the floor. When the fame cord is drawn the reverfe way, each curtain flies open, and comes to their place on each fide, as they are now reprefented. The cord pafTes on a fide pulley fixed on the right-hand. To ^ ( 409 ) To effect this, the rod is made in. a particular manner, having two pulleys at one end, and a fingle one at the other, which cannot well be defcribed in words without a drawing of it. Of the Gentleman^ s Secretary. Plate LIT. This piece is intended for a gentleman to write at, to keep his own accounts, and ferve as a library. The ftyle of finifli- ing it is neat, and fometimes approaching to elegance, being at times made of fatin-wood, with japanned ornaments. Of the manufaBuring Fart. The great thing to be obferved in this, is the management of the fall A, or writing part, which is lined with green cloth. This fall is hung by an iron balance-hinge B, fo that when the fall is raifed vip by the hand a little above an angle of forty-five degrees, or in the pofition it is fliewn at A, it falls to of itfelf by the balancing power of B. When A is in a horizontal pofition, B is at F, the infide of the pilafter, on which is glued a piece of cloth to prevent the 3 F iion ( 4'o ) iron from rattling. B flopping at F it is evident how firmly the fall is fnpported by that means ; for the hinge is made very ftrong, about three (juarters thick at the dove-tail end, and ta- pered off to about a quarter thick at the joint, and where it is fcrewed to the fall. The hinge is made in two parts, as D and b. D has a center pin, and is fcrewed on to the infide of the pilafter, as at ^; /^ is all in one piece, and is fcrewed on to the fall, having a center hole to receive the abovementioned pin in the other part of the hinge. It is neceffary to obferve, that there is a vacuity behind both the upper and lower pilafters in which the iron ba- lance operates, fo that nothing is feen but the mere joint of the hinge. Again, it is requifite to obferve, that a hollow muft be worked on the upper fide of the under carcafs, to give place to* the circular motion of the under angle of the fall, as it turns upon its hinge from a perpendicular to a horizontal form. This hollow may be obferved in the plate. The fpace i contains the fall when it is up; 2 is an open fpace, which affords room for the rings on the fmall drawers; and 3 is the pilafter. The or- namented freeze under the cornice is, in reality, a drawer, which fprings out when the bolt of the fall-lock is relieved. This is done by a fpring-bolt let into the partition under the drawer, A^/.C. />/■/■ Platr 63. A Cii^irrBJEK ^yASH"HArra) Tabjle T .fJirratfri <irl Pithlu^hd tUf thf Act du-ecti hy (r.Tcrty June 2^.iJ<i2. ^ Bar ml j>*tlp ( 4" ) drawer, which is forced up by the bolt of the fall-lock into the under edge of the drawer; and when the fall is unlocked this fpring-bolt returns to its place in the partition, and a common fpring fcrewed on to the drawer-back fends it forward, fo that it may be drawn out independent of a ring or handle. When the fall is up, there appear two pannels in the form of thofe below. As for any other particular, it muft be under- ftood by a workman. Obferve, the dimenfions of every part may be accurately taken from the profile by the fcale. Of the Cylinder Wajh-hand Table. Plate LIII. These are always made of mahogany, and having a cy- linder to rife up to hide the wafliing apparatus, they look neat in any genteel drefling-room. They alfo contain a bidet on the right near the front, and D, a water-drawer on the left near the back, fo that when the two are puftied home they pafs by each other. The drawer on the front, which appears partly out, runs above the bidet and the water-drawer. The two heights of fliam drawers above contain the cylinder, and the two heights of fliam drawers be- 3 F 2 low ( 412 ) low contain the bidet and water-drawer. The bafon has a phig- hole at the bottom, by which the water is conveyed off into the ■drawer D, which is hned with lead. The top of the cittern is hinged, and can be turned up at any time to fill it M'ith freili vater. The glais rifes up behind, in the fame manner as that of a fhaving-ftand. And when the glafs is down, the top can be turned down alfo; and the cylinder being raifed to meet it, the whole is enclofed. The motion of the cylinder is guided by two quadrant pieces, one at each end of it, which are hinged to the top in which the bafon hangs. This is fliewn by A in the profile; which, when the cylinder is let fall to its place, will be at B. When the cylinder is raifed up to A, it catches at C, which is a fpring of the fame kind as thofe put on to fecretary drawers. The bidet-drawer is fometimes made to take quite out, having four legs to reft on. The end of the piece of work is cut out fo as the feet can go in without being folded up. This, in the defign, is ftopped from coming quite out, and the framed legs, which appear, fold under the drawer and flip in along with it. Of the Pembroke Table and French Work Table, Plate LIV. The ufe of this piece is for a gentleman or lady to break- faft on. The ( 413 ) The flyle of finifliing thefe tables is very neat, fometimes bordering upon elegance, being at times made of fatin-wood, and having richly japanned borders round their tops, with or- namented drawer- fronts. The manufadluring part of this table differs but very little from thofe in common ufe. The fly brackets which fiipport the flaps are made and fixed in the fame manner as any other, only I apprehend it belt to make a dove-tail groove in the front for the drawer fides, at a diftance from each end of the drawer-front equal to the thick- nefs of the bracket and the inner lining ; fo that the front laps over and covers the whole, as appears in the defign. In this cafe the lock-bolt flioots up into the top of the table. The top and frame may be connected to the pillar and claws, either by a fquare block glued up, or by a couple of pieces, about four inches broad, half-lapped into each other at right-angles, and double tenonned into the pillar, and fcrewed to the bottom of the frame, as the profile of the pillar and claw is intended to fuggeft. The workman is defired to obferve, that the top of the table, as fliewn in the deiign, is not meant to reprefent a regu- lar ellipfis, as they are generally made a little fuller out at each corner ( 414 ) comer of the bed. The reafon of this is, that the flaps, when turned down, may better hide the joint rail. Of the French Work Table. Plate LIV. The title of this table fufficiently indicates its ufe. The ftyle of finifhing them is neat, being commonly made of fatin- wood, with a brafs moulding round the edge of the rim. The front part of the rim is hinged to the top, in the fame way as the front of a fecretary or defk-drawer ; fo that when it is turned up, it fallens by two thumb-fprings as they do. The brafs moulding is mitered upon the edge of the rim when the front is up, and after it is hinged ; which being cut through with a thin faw, the moulding, on the return of the front, will be fair with that on the end. The flielf below is fliaped fomething like a boat. The bottom of it is made of inch fluff, and double tenonned into the ftandards, as the profile plainly fliews. The top of each fland- ard has alfo double tenons, to which crofs-bars are morticed and fcrewed to the under-fide of the top. The fcale fliews the proportions of the ftandard, and the height of the table; its breadth is fourteen or fifteen inches. I The ( 4^5 ) The boat part, which ferves as a convenience for fewing imple- ments, is fix inches over the middle, and three at each end. I have, in thefe two defigns, introduced ftri6t fliadowing, that the learner may better judge of its efFe6^s in fuch cafes. — But I muft obferve the fliadows here are rather too faint, be- caufe 1 was afraid to make the plate look heavy. The fun's rays are here confidered parallel to the pi6ture, which is fully illuftrated by different cafes, in the Treatife on Shadowing, fee page 328. And, therefore, I fliall only obferve here to the learner, that, in making out the fliadows of objects, a harfli out- line ought carefully to be avoided. In fa61:, there ought to be no outline at all, except thofe firft drawn by a pencil to deter- mine the boundaries of the fhadow ; after which a large hair pencil fliould be ufed to fill up the fliadow. We may likewife remark, that if Nature be obferved duly, fhe teaches us that the fhadows of obje6ls are flronger nearell: the foot or place where they reft, and grow fainter the further they recede from the foot of the obje61:. The reafon of this is : becaufe if fliadows are very long, as from a houfe, there is a ftrong refledion of light towards the boundaries, which mixes with the fliadow, and confequently weakens it. It is fomewhat fimilar to what aftro- nomers term a penumbra, or imperfed: fliadow accompanying a total one. Laftly, ( 4i6 ) Laflly, it may alfo be obferved, that when an objeil is to- tally immerfed in the fliadow of another, as the table claws are in the Ihadow of the top, there is a fort of additional fliadow, occafioned partly by refle6tion, and partly by the conta6t of the two furfaces, but thefe are fliort and imperfedl: in their boun- daries. Of the Tripod Candle-Stand. Plate LV. These are ufed in drawing-rooms, for the convenience of affording additional light to fuch parts of the room where it would neither be ornamental nor eafy to introduce any other kind. The ftyle of finifliing thefe for noblemen's drawdng-rooms is exceeding rich. Sometimes they are finiflied in white and gold, and fometimes all gold, to fuit the other furniture. In inferior drawing-rooms they are japanned anfwerable to the furniture. Perfons unacquainted with the manufafturing part of thefe Hands may apprehend them to be flight and eafdy broken ; but this objedion vaniflies, when it is confidered that the fcrolls are made of Itrong wire, and the ornaments cemented to them. 3 I could ( . ^™,4.pl.7 ' y/y//f'^/ C az/r///" ' ^/r/ //(■/■> J'latf . .y,; V? S/in-nten Jfcl. Tnbh//ud ru l7if > ict tiirec'tj; hv <^' Te?rv- ■ hilr- 2 /. 1J,JZ . , Jjiir/rn' A'cllTp. ^ MAMZMQlTJjy J^EM^HOJ^^ Jl-iBii: . /.Li/p •' I'^i-iy.J-fuuA. Pul/iAc^ /j 7:SA^m/?^n JUr'H (^C) -2. . \ ( 4^7 ) I could not fhew to advantage more than three hghts, but, in reahty, there are four ; one at the center, and one at each angle. The top of the left ftand is a round vafe, which can be turned and have the fquare handles put on afterwards. The handles fhould be placed parallel to two of the feet. The top of the right one is a concave fpherical triangle, having all its fides equal. As to any other part, the workman's own notions will fug- geft every thing neceffary in their manufa6lure. Of the Harlequin Pembroke 'Table. Plate LVI. This piece ferves not only as a break fall, but alfo as a "writing table, very fuitable for a lady. It is termed a Harlequin Table, for no other reafon but becaufe, in exhibitions of that fort, there is generally a great deal of machinery introduced in the fcenery. Tables like this have already been made, but not according to the improved plan of the machinery here propofed. In this, however, I alTume very little originality or merit to myfelf, except what is due to the manner of fhewing and 3 G defcribing ( 4i8 ) defcribing the mechanifm of it : the reft is due to a friend, from whom I received my firft ideas of it. The particular advantages arifing from the machinery arc as follows : Firft, the neft of drawers, or till, fliewn in the defign, can be raifed to any height, gradually, imtil at length the whole is out. Second, when the whole is out, as reprefented in the defign, it cannot be taken away, becaufe of three ftops which keep it in; two at one end, and one at the other, according to the grooves in No. i. Thirdly, but if neceftity require that the till ftiould be taken quite away from the reft of the table, in order to come at the machinery, then one of thefe ftops at one end is fo conftrudled that it can be flipped back, and, the till being raifed up at the fame end where the ftop is flipped back, the two at the other end of courfe will relieve themfelves, fo that the till can be taken quite away. Fourthly, when the till is replaced, the ftop can be puflied into the groove again by the finger, which returns again into the groove by the force of a fmall fpring. Fifthly, ( 4^9 ) Fifthly, The till being let down again until it is perfeaiv even with the reft of the table-top, it can then be fecured in its place by means of another flop at the bottom, fo that if the whole table were turned upfide down the till would ftill keep its place. Sixthly, although the till be raifed and lowered by turning the fly-bracket which fupports the flap, yet the bracket is made to lofe this efFea or power by the turn of a key, and the bracket may then be drawn out to fupport the flap without raifmg the till,, and the table can then be ufed, as in common, to breakfaft upon. Thefe are all the advantages that are neceflary, or that can be looked for, in tables of this fort, to render them complete, and to obtam the approbation of the ingenious. But it will now be requifite to fliew in what manner the machmery operates fo as to efFe6t thefe ; and, Hkewife, to give fome defcription of its parts, that the workman may be able to form a proper idea of the whole. The firft and great thing to be attended to is, to fliew the manner of raifing the till by turning the fly-bracket. To ac- 3^2 complifli ( 420 ) complifh this, I have given a perfpe6live view of the whole machinery at No. i. Suppofing the till to be taken out, and the fly-brackets and inner lining away from the framing ; ab'i'i an upright iron axis, made in two parts, and conneded together by a round pin at the joint b ; of courfe, if the winch c be turned round, the axis a will turn round with it by the above pin, without moving the lower part of the axis b. Whence it is evident, that if the winch c be fcrewcd to the under edge of the fly-bracket, which bracket is fhewn in the defign, it will turn round without afFeding any part of the machinery. This is the caufe why the flap of the top can be up whilft the till is down. But if the fquare focket a be prefled down paft the joint b, the two parts of the axis will then be confined together, and therefore if the winch c be moved this way, it is evident that the machinery will inftantly be put in motion in the following manner : The winch c being fcrewed to the fly-bracket, and turned fquare out, it defcribes by its paflage a quadrant of a circle ; and the arm s of the crank-rod being fixed faft into the fame axis a b^ confequently it will defcribe the fame curve as the bracket: and as the crank-rod R is jointed into its arm at s and at /, in moving the arm the rod R is puflied forward toy, and the hori- zontal cog-wheel H of courfe turns to the left-hand on the cen- ter C. It being then turned to the left, as expreflTed by the dotted ( 421 ) dotted line at q, it follows that the upright cog wheel N mull be turned to the right-hand; and if this be turned to the right-hand, then mull alfo the quadrant cog-wheel Q on the left turn to the right with it: and, becaufe the axis A is fixed fall in the wheel Q, and the crooked levers e e into A, confequently the rollers L L, fixed by the rod o to thefe levers, will defcribe a quadrant of a circle, as denoted by the dotted line and the roller 9 ; becaufe the conne6ting cog-rod c makes Q move in the fame curve as N does. Again, if N, the upper part of the upright cog-wheel, move to the right, then mufl M, the lower part of it, move to the left; and, being con- necSled with the cog- rod 6, and it again to the right-hand qua- drant cog-wheel Q, it follows, as before, that the levers//, and the roller L, will defcribe a quadrant of a circle to the left-hand, as at 8. The reader mufl eafily fee now, that when the winch c is turned by the fly-bracket, that every part of the machinery- will be pint in motion, and that the levers and rollers, in ap- proaching gradually to 8 and 9, mufl neceffarily raife up the till. But it mufl alfo be obferved, that the motion of the levers // and ^ ^ is greatly promoted by the power of the common fleel-fprings S S ; for, when the till is down, thefe are always charged ; that is, the fides of the fprings are nearly clofe to each other, and thefe being connedled with what may be termed the auxiliary, or affiflant cog-rods, 4 and 7, and confequently prelT- ing againfl their ends, the quadrant cog-wheels Q Q are there- by made to revolve, and the levers and rollers are raifed almoll as ( 422 ) as much by this means as by the other machinery. It mull alfo be noticed, that as thefe fprings and auxiliary rods greatly affift the other power in raifing the till, fo do they alio check the fudden fall of it, by a conftant refiftance againft the prelTure of it, fo that the palTage of the till downwards is made by this mean fmooth and eafy. Obferve, p,p,p,p, are brafs pulleys fixed to keep the cog- rods in their place, and zv w are pieces of wood to keep the fprings firm to their center. The reafon why there are but three rollers, and two of them at one end, is obvious; becaufe the till muft reft truer on three points than on four. It cannot totter on this account when it is fully raifed, becaufe there are two ftops at that end where there is only one roller, which nm in the grooves G G ; and if the ftops chuck up to the end of the grooves when the till is up, it is impoffible that it can totter, confidering that the other end i& upon two rollers. And here let it be noted, that if the work- man find any inconvenience owing to the double roller o being at the fame end with the axis d b, it can be removed by putting the double roller where the fingle one is, which makes no dif- ference with any other part of the machinery. And obferve, that when the rollers are nearly perpendicular to their axis A A, they enter upon an inclined plane, or on thin pieces of wood planed C 4^3 ) planed ofFlike a wedge, of the width of the rollers, and whofe thin end is glued to meet the rollers as they rife, fo that the till can thereby be raifed as high as we pleafe. Thefe wedges being glued on the under fide of the till to fuit exactly the place of the rollers, the projed:ion of the wedges below the till makes it neceflary that there fhould be a vacuity in the axis A A, for them to fall into when the till is down ; becaufe, in this fitua- tion, the till refts on the three rollers, which are nearly on a level with the axis A A. And as the wedges above mentioned muft lie acrofs the axis A A when' the till is down, every work- man muft fee the neceffity of a vacuity, or otherwife the till would not fettle to its place. The next thing in order is to fhew how one of the flops can be relieved, or flipped back, fo that the till may be taken quite away. The conftru6lion of this flop is fliewn by No. 4, which fuppofes that we fee the under-fide of the till. A is a hole cut through the till, which hole is drawn by a compafs, having one foot at C the center. P is a round pin, which comes through to the infide of the bottom of the till. K is a tin key which hooks this pin. In applying this key to the pin, the writing ilider, fliewn in the deflgn, muft be puflied in, and the front- part which covers the letter holes turned up to its place ; and there being a groove acrofs the under flde of the Aider, exailly 3 where ( 424 > where the pin comes, and the Aider giving a little way for the thicknefs of the aforefaid key, the groove jiift mentioned admits the key over the head of the pin P ; then, when the key is drawn back again, P moves toward A by the center C ; and S, the flop which proje(5ls beyond the till, is by this mean drawn within. B is a plate fcrewed on to the till to keep the flop firm. Again, when the till is down to its place, it is neceflfary that it fliould be flopped there alfo, as has been already faid. The apparatus for this is fhewn at No. 3, which is a different view of the fame lock as at No, 2. i, 2, 3, 4, is fuppofed to be a part of the bottom, not of the till, but that whereon the machinery is placed at No. I. / J is a kind of trammel with flits in it, moving on a center at s. A pin is fixed to the bolt of the lock, and there being a pafTage for the pin cut out of the lock-plate, as fliewn in the defign, this pin moves up and down, according as the key is turned. ^ is a kind of lever, with two arms, moving at the center a. c c are ftaples which are faflened to the under- fide of the till, and as the bolt of the lock llioots downwards, the trammel ts throws the arms of the lever out of the ftaples which are fixed to the underfide of the till ; by which means the till is relieved, and can then be raifed by drawing out the fly-bracket. And here the workman muft be careful to ob- ferve, that when the bolt b. No. i, is fhot, as it now appears, the till is always relieved, and the bracket at the fame time has power ( 425 ) power to raife the till ; becaufe the fork D works in the groove d oi the axis ab zt No. i, and thereby prefles the focket a to b^ and gives the winch c power over the machinery. And obferve further, that when the bolt b at No. 2 is up, as it is Ihewn at No. 3, then it is evident that the arms of the ftop-lever will pafs through the beforementioned ftaples at the under fide of the till and fecure it, while, at the fame time, the bracket will lofe its power over the machinery; becaufe the focket a, at No. I, is thereby raifed above b^ and of courfe as b turns on a pin, the winch c cannot affect the crank-rod s R, and therefore no part of the machinery is moved. Thus it is, I think, fufficiently clear that the till can be flopped and relieved when it is either up or down, and alfo that the bracket can be drawn out to fup- port the flap, while, at the fame time, the till is both down and flopped, fo that the whole may be ufed as a common breakfaft table. It remains now to give fome hints refpedting the manufac- turing part. Of the Table Top. The fize of the table when opened is four feet, and two feet feven inches long ; and the rails eight and a quarter deep. 3 H The ( 4^6 ) The whole top is divided into four compartments, to anfwer the opening for the till. Round thefe compartments is a japan- ned border, to fill up the fpace which lies between the end of the table and the end of the till. This border muft be continued all round alike, to make the pannels appear uniform and of equal fizc. The bed of the top fliould be framed in two pannels of three-quarters mahogany well feafoned, and the breadth of the fliles to fuit the opening of the till. A pannel of half-inch fluff fliould be tongued into the other part of the bed where the till does not rife. Then, for the fake of the allragal which is to be worked on the edge of the top all round, a piece fhould be tongued in, the long way of the grain, into each end of the bed. And obferve, that as the bed of the table will frequently have to be taken off in the courfe of the work, it is heft to put fmall tenons into the under fide of it, and mortices into the rails all round ; by which means the bed w ill be kept to a certain place, and taken eafy off at any time. A black firing is put next the till, all round the infide of the border, to hide the joint. In put- ting this black firing on at the opening of the till, the infide of the mahogany frame fliould be rabbetted out to take a flip of black veneer about three-eighths wide; and it being left to ftand above the framing the thicknefs of the veneer, this black flip can be fhot by a rabbet-plain to the thicknefs of a neat firing, and the veneer muft be jumped to it. The ufe of this is, that when the till rifes it may not take any part of the firing away with ( 427 ) with it, which it certainly would do if it were put on merely as a corner firing. Of the nil. The carcafs of the till is made of half-inch mahogany; the partitions and letter-holes of thin quarter ftuff, and black beads put on their edges, all of which muft be kept back about half an inch from the edge of the carcafs, to give place to the writ- ing Aider; part of which turns up as a front to the infide of the till, and part of it remains in it: and, as a part of the writing- llider remains in the bottom of the till below the drawers, con- lequently there muft be a joint in the Aider to anfwer it; which joint is hinged at each end, before the crofs-band is put on for the green cloth. The workman may make the hinges himfelf to fait that purpofe. They may be made as common delk-fall hinges, only the knuckles of the hinge are made a little higher than common to receive a thin veneer; which, when fcrewed on, the veneer for the band of the cloth lies upon and covers the ftraps, fo that a part of the knuckle is only feen : but ob- ferve, that the ends of the veneer, each meeting at the knuckle, muft be cut in a floping diredion, fo that they and the brafs knuckle between them will be exadly in the form, and of the fame nature, as the rule-joint of a fly-bracket for a Pembroke 3 H 2 table ; ( 428 ) table; and therefore it muft be evident to every workman that the front will turn up fquare. The Aider is topped into the till by a couple of pins which run in grooves; and when it is puflied home, before it can turn up, a hollow muft be worked in the bottom of the till, to give room for the angle of the rifing part of the Aider to turn in. When the Aider is turned up, it is kept in its place by a fpring-catch, which ftrikes into a plate put on at the under fide of the top of the till. And obferve, that when the front is up, it Aiould be rather within the carcafs of the till, both for the purpofe of letting the till go eafy down, and to admit of a Aip of thin green cloth at each end, fo that when the front is turned upon the top of the Pembroke table it may not fcratch it. Another method may, however, be propofed, and which will be attended with lefs trouble; only with this difadvantage, that it takes off a little of the height of the drawers. The Aider, being made in two parts, may be hinged in the manner of a card-table top, which, when it is folded over, can be puAied to its place. But obferve, that the under top muft be made fo much broader than the upper one, as will admit of its being flopped in after the manner of the other; fo that when it is drawn out, the upper top will rife and clear the drawer fronts. If the Aider be made in this manner, the drawers can then C 429 ) then be brought within a Httle of the front edge, and what re- mains ferves to give place to a couple of thumb-nail holes to draw out the Aider by. N. B. The profped; door is made to run in at the top like a drawer, upon the fame principles as the front of the cabinet in Plate L. Of the Frame of the 'Table. The legs are made a little ftronger than ufual, becaufe the table is pretty heavy altogether. Both the end rails are divided into four drawers each, in appearance; but, in reality, there are but two in the whole: for obferve, that, for the fake of flrength in the frame, the lower drawer of the left hand is made real, and that above it is a ftiam ; but at the other end, which is not feen in the defign, the upper drawer is real, and the under one a fham. A middle rail is tenonned, of inch fluff, into each end rail. Againft this rail the upright part of the machinery is fixed, as fhewn at No. i; and as this rail ftands within the edge of the top framing about an inch, it contains the whole projection of every part of the machinery, fo that the till pafTes without obflru(5tion. The ( 430 ) ^ The inner lining for the fly-brackets to fall againft, is not lefs than three quarters thick when planed; and it muft be the whole breadth of the end rails, i. e. eight and a quarter. The fly-bracket makes up the remaining thicknefs of the foot, and comes down low enough to anfwer the height of the upper crofs-band of the lower drawer. The part remaining below the bracket is veneered the whole length with fatin-wood, and crofs-banded to match the drawer fronts. The workman, in making the fly-bracket to which the winch c is fcrewed, muft obfcrve to make a flioulder pin on the turning part of it at the under edge: and this flioulder will require to be double the ufual thicknefs, that the iron winch c may be let into the bracket without injuring the rule-joint, or interfering with the wire of its center. The lock, at No. i or 3, is put on at the infidc of the inner lining, fo near to the axis ab, at No. i, as that the fork D of the lock fliall extend to the groove d in the focket of the axis a b, which then will determine the place of the key-hole, as fliewn in the defign. Of (7i2lr/'i ■ j'l'f/^. A''"/ />/ ' (^^/■//a///^/// /('/■ a ^^r/r~i (>/• '^/ff/'/r^ ;,/ .!r: r..u.-,.,f„„ ././.,, />J/,ri,../ .,.■ rl. ./,/ ,/,r,,-/.r f'./ru_/yi/,A- If.lW r. 7*/v-i-^<v/^. /K V ././. / TSMMEJVm /orMooKfASES M''Z 'W« •■!««« TSh^ratcn.iip/ &Tfrrtf,S,'u!/l J'u^/iyh'ff i'if ir 'Jhr'n^. ^e.-^^y*ft . ( 431 ) Of the Pediments. Plate LVIf. With rcfpcd to thefc pediments little can be faid, as the de/igns themfclves Hiew in what manner they fliould be exe- cuted. No. T. Should have the facia, or ground board, glued up in three thicknefres, having the middle piece with the grain right up and down. The foliage ornaments are cut out along with the aftragal, and planted on; and the whole may eafily be made to take off from the cornice, by having a tenon at each end and one in the center. N. 1. The tablet part is intended to have a crofs-band round it, and the drapery may be japanned. The aftragal on the top of it is meant to return over the ogee. The fquare of the ogee may come forward, level with the tablet, to prevent too great a projedlion. No. 3. In the center there are two pilafters to proje<St a little from the ground, which are fluted. The pannels at each end arc intended to be fanned the reverfe ^yay, or with the rounds out. No. 4. ( 432 ) No. 4. The fcrolls are continued in one piece from the foU- age, and planted on. No. 5. The center is intended to be veneered and crofs- banded, with an oval let in, and japanned. The pedeftal above is intended to be thrown back, in a hollow carved in leaves. The foliage on the fcrolls is meant to lap on the aftragal, and to finifh off at the patera. The ground of the facia is fanned out. Of the Cornices. Plate LIX. In thefe cornices the fpring is fliewn, and the proper gaging is pointed out. The width and thicknefs alfo of the mahogany is fliewn. The aftragal, in No. 3 and 5, can be worked feparate, and glued on afterwards. The pateras, in No. 6, are turned and planted on. Of the Method of gaging and working Cornices, The explanation of this may be thought, by fome, an un- neceflary bufinefs ; but from the bungling manner in which I have feen many workmen proceed to ftick cornices, I am cer- tain Nfijplz COT^A^ICAJS d SZ/J^BASKS, . MM , I Sheraton J^/ JuUt'Ai/ ,ur r/,rArf t/.'rrch-.lif o.Tfirry. (?ef:'l6j^^i. rf^Jryj'.'CwA ( 433 ) tain that a few hints will be of fervice, efpecially to the inex- perienced. For this purpofe I have, in No. i, lettered each gage-point, and I fliall proceed, as fuppofing that it is neceffary that the whole fliould be taught. When the pattern of any cornice is given to be worked, t^ke the drawing and ftrike a line a n to touch as near as may be each member. From this front line ftrike one at each end fquare from it, fo as to take in the whole extent of the cornice. Then draw another line parallel to that on the front, to fhew the neceffary thick nefs of the mahogany, and proceed as fol- lows : Let the fluff be fawn out broad enough to plane to d o; after which, plane it true on both fides, and glue on deal of the breadth of e p, and thick enough to make out the whole fpring of the cornice. After the glue is dry, plane the mahogany to the exa(5t breadth of d o. After ftriking a fquare line acrofs the mahogany, extend the compaffes from a to a^ and to c^f^g\ Sec. and lay all thefe points on the fquare line, and run a gage thro' each of them. Run then a gage from a to b^ and from ntoo; and taking a bevel, fix the handle of it exactly by the front line, and let the infide of the blade of it correfpond with o p. With the bevel thus fixed, plane down the wood behind till it fit the bevel in every place, and be brought down to o. Take 3 I then ( 434 ) then a fqnare, and plane down the wood at b and e till the fquare fit in every place, and the wood is brought down to b. After this lay the cornice on the fide o />, and flioot off the wood ci,a^b\ then lay it on the fide b <?, and flioot off the wood zt n o to m. The cornice being thus properly fprung, faften it down on the fide a p, and proceed to rabbet out the feveral fquares. Begin at c and rabbet down to /; at b run on a fide gage, and, enter- ing in by a fiiipc's bill, work down to /, the fluting being laid on afterwards ; at q run on a fide gage each way for the fquare of the ovalo. From / rabbet dowai to X', and at / down to m\ and thus it is evident that the whole cornice, of whatever kind, cannot fail of being correctly worked. Of the Method of conira&ing and enlarging Cornices. SupposEAtobea cornice already drawn or worked, and it be required to draw and work one a third, fourth, or any other proportion narrower than A, and at the fame time, to contract its projecftion in proportion to its height : Take the compafles and extend them to a o, the whole height of the cornice A, and with this opening fweep an arch each way, and where they interfe(5t, to that point draw right- lines from and «, forming an equilateral triangle. In the fame manner ( 435 ) manner proceed with the projection of A, as fhewn in'the figure. To the fummits of thofe triangles draw Unes from the feveral heights and projections of each member. If the cornice to be drawn is to be one third lefs, then divide any one fide of the triangles into three equal parts, and take one part from o to />, and let fall a perpendicular from p ; and from where this per- pendicular cuts each line draw parallels, which will give the height of each member in exaCt proportion. For the proj edi- tions : ^ is one third of the fide of the triangle, as before; draw a parallel line at q, which will give the feveral projections fought. Take q t, and transfer this to p r, and fo of the reft, till you have laid on each projection : after which let fall per- pendiculars, as Ihewn at No. 7, and proceed to draw the out- lines of each member within their proper fi:juares, and the cor- nice will be contracted in the moft accurate manner. Of enlarging Cornices. Suppose now the cornice A is required to be higher than what it is at prefent. Draw parallel lines from each member^ and having fixed the compaffes to the height propofed, fix one foot at 0, and move the other till it touch any where on the line a k, as at /^; draw a line from c to k^ and where this line inter- feCts with each parallel before drawn, will be the feveral heights 3 I 2 of ( 436 ) of the mouldings as required. To find the proje6lion, proceed thus: — fvveep the arch a c, cutting ok 2iX.b\ take a b and place it from c to d^ and from d draw a line to o, and o m will then be the whole projection of the cornice proportionable to the height k\ confequently where the line o m interfe6ts, each perpendi- cular raifed from the feveral projedlions of A, will be the feveral projedlions fought, o m is then a fcale line for the projecStions, and k for the heights of each member; and having thefe, the cornice can then be drawn on a feparate paper, in the fame man- ner as A was drawn at firft. By continuing the parallel lines of A to the right, as fhewn in the plate, and by letting fall its perpendiculars to any length, it is evident that A may be enlarged as much as we pleafe, by drawing the line o k more oblique, as at ^, which then makes it rather more than one third higher. Then, by extending the compafTes from a to where o e cuts the arch, and by replacing this opening from c to g^ and ftriking a line from o to g through to/, o/ will be its projedlion as before; on which principles of will be in a ratio with o e. This the workman can prove, for by comparing o f with the length of the projedlion of A, he will find it rather more than one third longer; and by com- paring e with «, he will find it rather more than one third longer alfo. Thus P/.rfr lli\ '^ ^^^i /////,! ^\J.'rt^/^furir^/>r?,/ yy/v/^/7 » /^-'/'/^ ,o ^ &" -^. t.J^^f'^///t(7t4/.f'4ftYr /// r////////f<^n rym/' t.y^/^fre (^Wf7/r^^. ' ' I ' I ' T" /.v/ rM^,.,ii>, /).■/, /^.r-/-"- /!«//-. JiiAf^TK-daj l/u-^Af .6>.:/j./'<- t7.Terrv . /,m'. 16.17.) i. ( 437 ) Thus it is evident that any cornice or moulding whatever, and however complex, may be contradted and enlarged as we pleafe, and that with the greateft mathematical nicety. Of the Ladfs Drawing and Writing Table. Plate LX. These tables are finiflied neat, either in mahogany or fatin- wood, with a brafs rim round the top part. The upper part is made feparate from the under part, and fixes on to it by pins. The rifing defk in the middle may be made to Hide for- ward*, which will then ferve to draw upon; and the fmall drawers below the coves at each end will be found convenient for colours. The drawer in the middle of the front ferves to put the drawings in. The top is lined with green leather or cloth. The fcale fhews the fize of every part in the front, and the breadth is two feet three inches. The height of the upper part is eight inches. * See the diredlions given for the Kidney Table. Of ( 438 ) Of the Dining Parlour. Plate LX. This method of reprefenting a dining or drawing-room has its advantages; though the moft general method is by a plan and fed:ion, as the drawing-room in Plate LXl. In this method the end wall neareft the eye is fuppofed to be laid level •with the floor, without which the infide of the room could not be feen. The advantage of this is, that the walls, furniture, and every particular, are fliewn in their natural pofition, except the firft end, fo that the efFedt of the whole may be better judged of than in the other method. The advantage of the method in Plate LXI is, that the fides and ends of the room being turned down, from a geometrical plan, every thing on the walls is fhewn geometrically, and therefore the parts are more diftindt ; but with this difadvan- tage, that it muft be viewed at four different times, by turning each end and fide to the eye; whereas, in the other way, ,the whole is feen at one view. In proceeding to draw after the method of Plate LX, make a fcale of feet as there fhewn, and draw G R for a ground line, and H L for the horizon. Let the center of the picture be in the ( 439 ) the middle of the end; and, as thefe are views of a fliort dif- tance, extend the compaffes from the center to o, and turn it up to d^ which will be the fliortefl diftance that can be applied. Draw vifuals from o, r, b^ a^ to the center. From o to i lay on the fize of the firft pier, and draw a line to d^ which, cutting the vifual drawn from o to the center, gives the perfpeflive of it. Then lay from i to 2, the breadth of the window, and draw a line to d\ and in like manner find the appearance of all the piers and windows. Obferve, that a line from R to a^ finds the whole length of the room. How every other part mufl be drawn will be obvious to every one who underftamls perfpec- tive, and no other with any propriety can attempt it. This dining-parlour gives a general idea of the Prince of Wales's in Carlton Houfe; but in fome particulars it will be a little varied, as I had but a very tranfient view of it. The Prince's has five windows facing St. James's Park. This alfo has five, one of which is hid by the left column. His win- dows are made to come down to the floor, which open in two parts as a double door, leading to a large grafs plat to walk in. If I remember right, there are pilaflers between each window; but this is intended to have grafs. In his is a large glafs over the chimney-piece, as this has. To thefe glafs frames are fixed . candle-branches. At each end of his is a large fideboard, nearly I twelve ( 440 ) twelve feet in length, (landing between a couple of Ionic co- lumns, worked in compofition to imitate fine variegated marble, which have a moft beautiful and magnificent effect. In the middle are placed a large range of dining-tables, ftanding on pillars with four claws each, which is now the fafhionable way of making thefe tables. The chairs are of mahogany, made in the flyle of the French, with broad top-rails hanging over each back foot ; the legs are turned, and the feats covered with red leather. I could not fhew the curtains of each window without con- fufion, but they are of the French kind. Many dining-rooms of the firfl nobility have, however, only two columns and one lideboard ; and thofe of lefs note have no columns. The general ftyle of furnifhing a dining-parlour fhould be in fubftantial and ufeful things, avoiding trifling ornaments and unnecelTary decorations. The pillars are emblematic of the ufe we make of thefe rooms, in which we eat the principal meal for nature's fupport. The furniture, without exception, is of mahogany, as being the moft fuitable for fuch apart- ments. Of C 441 ) Of the Drawing Room. Plate LXI. In drawing a room of this kind very little perfpe(5tive is wanted. All that is required is a horizontal line on each wall. And I would not advife drawing every object on each wall to one point of fight, as thofe at the extremities will thereby be- come exceedingly diftorted and unnatural. For, upon fuppo- fition that the fpe6lator moves along to different ftations as he views any one fide of the room, perfpecStive will admit that the defigner have as many points to draw to as the fpedlator had ftations to view from. If a room of this fort be narrow, fewer points may do for the furniture at each end, with a little ma- nagement ; but the furniture on the fide walls fhould have al- moft as many points as pieces of furniture. The line that marks out the boundaries of the floor, ferves as the proper ground line to each horizon, and the geometrical meafurement of each piece being taken from the fcale and laid down on the wall, the per- fpe6tive is drawn from each point backwards, or into the room. A drawing-room is of that fort which admits of the higheft tafte and elegance; in furnifiiing of which, workmen in every nation exert the utmoft efforts of their genius. 3 K To ( 442 ) To aflift me in what 1 have here fliewn, I had the oppor- tunity of feeing the Prince of Wales's, the Duke of York's, and other noblemen's drawing-rooms. I have not, however, fol- lowed any one in particular, but have furniflied my ideas from the whole, with fuch particulars as I thought belt fuited to give a difplay of the prefent tafte in fitting up fuch rooms. ><► It may not be amifs to mention fome particulars refpefling the Prince's room, that the reader may form fome idea of its tafte and magnificence. Its proportions are as follows: — forty-eight feet fix inches long, thirty-four broad, and between eighteen and nineteen feet high, including the cove of the ceiling. It has five windows in length, a fire-place at each end, and five doors. Two doors are at each end, one of which is fham; and a large arched double door nearly in the center opi)ofite the windows. Oppofite each window is a large glafs, with a circular top, to fuit the arches above the windows ; and over each fire-place there is alfo a glafs. In the piers betw^een each window there are no glafles, but a couple of richly finiflied Corinthian pilaf- ters, w^ith their architrave and impofts to fuit the tops of each window. ( 443 ) window. On the fule oppolite to the windows the fame pilaf- ters are employed ; for, as the before-mentioned glalTes each oc- cupy a fpace equal to the width of a window, and are directly oppofite to them, this preferves a regularity in the pilafters on both fides. In like manner each end of the room has its pilaf- ters of the fame order, one on each fide of the fire-place, and of the doors. The cove and ceiling are richly ornamented in paint- ings and gold. A room of this defcription is not, however, a proper pre- cedent for drawing-rooms in general, as it partakes principally of the charadler and ordinance of aftate faloon-room, in which are entertained ambafladors, courtiers, and other perfonages of the higheft ftations. In the drawing-room which is here fhewn, every thing will appear eafily underftood to a workman in town, who is accuftomed to fee fuch apartments; but for a ftranger, and thofe workmen who refide in the country, it will be proper to point out a few particulars. The pier llibles have marble tops and gold frames, or white and gold. The glafles are often made to appear to come down to the ftretcher ot the table; that is, a piece of glafs is fixed in. behind the pier table, feparate from the upper glafb, which 3 K 2 then ( 444 ) then appears to be the continuation of the fame glafs, and, by refledtion, makes the table to appear double. This fmall piece of glafs may be fixed either in the dado of the room, or in the frame of the table. The arches above the windows are merely artificial, being only wooden frames put up, ftrained with canvas ; after which the fame kind of ftufF which the curtains are made of is formed to appear like a fan, and drapery tacked on to it. The pannelling on the walls are done in paper, with orna- mented borders of various colours. The figures above the glaffes are paintings in clare-obfcure. The fofas are bordered off in three compartments, and covered with figured filk or fatin. The ovals may be printed feparately, and fewed on. Thefe fofas may have cufhions to fill their backs, together with bolfters at each end. In France, where their draw- ing-rooms are fitted up in the moft fplendid manner, they ufe a fett of fmall and plainer chairs, referving the others merely for ornament. t The commode oppofite the fire-place has four doors; its legs are intended to fl:and a little clear of the wings; and the top is marble, to match the pier tables. In the freeze part of the commode is a tablet in the center, made of an exquifite com- pofition JVfSl.pl. I ( 445 ) poiition in imitation of ftatuary marble. Thefe are to be had, of any figure, or on any fubjedl, at Mr. Wedgewood's, near Soho- fquare. They are let into the wood, and proje6t a little forward. The commode fliould be painted to fuit the furniture, and the legs and other parts in gold to harmonize with the fofas, tables, and chairs. fo fupply the DefeH of Figure 32, Plate V. It is there fhewn how to find the miter of the fides of a comb-tray at any pitch, and of any given projecStion; but it was omitted to fhew how the miter is obtained in the thicknefs of the fluff, as it rifes to any pitch. Having found the breadth of the fides b c. Fig. 32, Plate V, with this opening of the compafTes defcribe a femicircle, fee Plate XXII, and make a e equal to the perpendicular height of the fide of the tray. Draw a line from e to the center ; and, parallel to this, fet off a line for the thicknefs of the tray fides, and the bevel of the under edge will be at 4. Draw a fquare at the center, the length of whofe fides fhall be equal to the thick- nefs of the tray fides, as 3, i, 2. Next draw the line B, A, E, pa- rallel to the diameter ; and take a e^ the fine of the angle of the tray fides, and transfer it to E A. From A draw a line to the center, cutting the fmall fquare at i, and the fpace i — 2 will be the miter fought for; that is, when the fides are mitered in their 3 ( 446 ) their breadth, according to Fig. 32, Plate V, fet a gage to i — 2, and run the gage along the miter, and plane it off to the gage from the outfide, and the miters will all come exadlly together. If the tray fides were raifed to b^ b i would then be the fine of their angle; and which being transferred to B, a line from B to the center cuts the fquare at 3; then is the fpace 3 — 2 the length of the miter fought. And thus it is evident, that as b advances to E the perpendicular, fo will the miter point B approach to D, the full miter. It is alfo evident, that -by this figure the miter of any thing not exceeding the diameter E of the femicircle may be found. For inftance, if the fides of any tray be half an inch thick, and it is required to be mitered and keyed together, draw a fquare of that dimenfion, as the fecond fhewn in the fi- gure; and if the fides bevel in an angle equal to the line ^, then I — 2 of the fecond fquare will be the length of the miter. I proved the truth of this theory by practice, and therefore the workman may depend on its infallibility; but he may eafily make the fame experiment himfelf. THE END. ERRATA. ^ Page 23, line 14, for b s, read b S. • 28, • 13, read it thus : — \i yon want five tentlis of a foot, and five of the hundredth parts of a foot, place your compafs foot — ___ il). ig, for any tenth part of an inch, read any one hundredth part of a foot. 57, 1<5, for 9, 5, read 7—5. ib. li, for (), 5, read q — 5. 61, 1 1, for a to «, read d to n. 70, 9, for the extreme line P E and P i, read P E and I I, . 137, 4, yir abacuo, rfW abacus. 152, Plate VIll, for 7 diameters, read 8 diameters. 16 i, line 22, Plate XII, for take wz 0, read take twice w a in the compaffcs, and with this opening find the center of the curve for the abacus as at p on *-ig. B. 206, 10, /or from a to a, read from d to a. 2 1 1 , 1 1 , fr Plate XV. read Plate XIV. 273, 15, for Fig. 23, read Fig. 21. APPENDIX TO THE CABINET-MAKER AND UPHOLSTERER'S DRAWING-BOOK. CONTAINING A VARIETY OF ORIGINAL DESIGNS FOR HOUSEHOLD FURNI- TURE, IN THE NEWEST AND MOST ELEGANT STYLE. ALSO, A NUMBER OF PLAIN AND USEFUL PIECES, SUITABLE EITHER FOR TOWN OR COUNTRY; TOGETHER WITH A DESCRIPTION AND EXPLANATION TO EACH PIECE. By THOMAS SHERATON, CABINET-MAKER: LONDON: PRINTED BY T. BENSLEY, BOLT COURT, FLEET STREET, fOR W. BAYNES, (SUCCESSOR TO G. TERRY,) 54, PATERNOSTER-ROW : SOLD ALSO BY J. ARCHER, DUBLIN; AND ALL OTHER BOOKSELLERS. 1802. J^.^2. fif.f. ^^ E LIP TIC BED F0RASINGX,E jLaDY JIL TSht'fa-ti'ri.cle/ /U/i/Ai/,^j- tAfAcl dirirts /y ffar.'Terry, Mj>- /■ //ip . ■iTinyS,u//i, APPENDIX. Of the Elliptic Bed. Plate I. of the Appendix. . As fancifulnefs feems moft peculiar, to the tafte of females, ■ I have therefore affigned the ufe of this bed for a fingle lady, though it. will equally accommodate a fingle gentleman.. . The elliptic fliape of the frame of this bed contrails its width at each end confiderably, on which account it will not admit of more than one perfon. On the manufadturing part of it I would offer a few hints to affift the workman. — The frame of the bedllead fhould be glued up in wainfcot three or four thicknefles, with the jump- joints crofling each otlier, as in the method of gluing the frames of circular card-tables, which fome ufe. For which purpofe, draw the full fize of the ellipfis upon a board, and make the diameters each way, by which one quarter will be 8 found. ( 4 ) -found. A thin mould muft then be made to agree with the quarter of the eUipfis, which will ferve for cutting out the •whole by, when different portions of it are fo taken as to form croffing-joints. The frame being thus made an entire ellipfis, as Fig. A. in Plate XXX. it is propofed to half-lap the pillars into the frame, and to have a ftretching rail at each end to tenon in oppofite to each pillar ; into which ftretcher the fere ws are to work which fix the pillars to the frame, as fhewn at <3r, b, c, d, in Fig. A. The workman will ealily fee that the frame made in this manner will not be defective in ftrength, nor in- convenient to move from one room to another. The fluffed head-boards at each end are framed feparate, and grooved into the pillars, with a tenon in their center to flip into the bed-frame, which can be eafily done when the pillars are fere wing to. The firft tefler which fixes on the pillars, fhould form an entire ellipfis to fuit the bed frame, and muft be glued up in two thickneffes of good deal or wainfcot ; to the edge of which fhould be glued two thickneffes of clean foft mahogany, of which to work the cornice, as expreffed by figure B, in Plate XXX. The ( 5 ) The fecond, or falfe tefter, is that to which the ribs of the dome part are fixed, as e in Fig.B; and /is an architrave which is bent round the infide of the firft tefter, and rifes fo high above it as to receive nearly the thicknefs of the falfe tefter ; fo that the architrave is a guide to the whole dome, and is fufficient of itfelf to keep, it firm in its place. With refpedt to the dome, it will be beft to make it in two parts. The cove part feparate, and the round or fpherical part feparate. This can eafily be done, by repeating the fame ope- rations as were necelTary for fixing and managing the cove part ; for it muft be obferved, that there is a light cornice or moulding where the circular part of the top begins, and which fixes on a tefter in the fame manner as the other. To the under fide of this cornice is the drapery, which hangs in the cove, tacked all round, as is the valence to the under cornice. The curtains are drawn up by pullies fixed in the under tefter, and thus forms a drapery, by being tied to the pillars with cords. The circular part of the top is intended to be pannelled out in gilt mouldings, which cannot fail of producing a fine efFe6l, particularly fo if the furniture and covering of the dome be light blue. The foliage ornament which runs round the under cornice, may be made either of compofition metal, or it may be cut in B wood, ( 6 ) wood, and fixed on wire, in the fame manner as the tops of ornamented glaffes are managed. Of the Ducbe/fe. The French have what they term diichefic beds, whence I fuppofe we have derived our ideas of a duchefle. What is fome- times named a duchefle amongft us, is merely two barjier chairs fattened to a ftool in the middle; fometimes, indeed, we add a flight tefler and covering, but even this is very different from theirs. The French duchefle beds are more fl:ately. The tefl:er is full and fixed to the wall, with drapery hanging down to the bedding and floor. The head part is formed fomething like the back of a chair ; at the foot there are fliort flump pillars; and the whole frame of the bed being detached from the tefler, may be moved to any part to loll upon. The ducheflle which is here given, is intended to anfwer three different purpofes. The ends, when detached from the middle flool, may ferve as fmall fofas. When they are connedted together without the tefler, and a fquab or cufliion made to fit over the whole, it will then ferve to reft or loll upon. When it is ufed as a bed, four fhort pillars are fcrewed to each back foot, and a flraight lath extends acrofs from pillar to pillar at each end. From thefe pillars are fixed the fweep iron rods which form the tefler, and which fupport the A DUCHESSE /'/ jt>-. ^ Sf^.ruri'n /J, Pui/is/u,if /;)• T. SA/raren M.iri-h ; ijip^ t',r/t/rtyr// />/r^r M ( 7 ) the drapery and covering which is thrown over the whole. The little dome or top is made feparate and entire of itfelf, with the cornice mitered round, and the tafTels fixed to it as fliewn in .the defign, and, the whole is placed loofe on without any faften- ings. They are made narrow, between t^yo and three feet wide, and feldom above it. Every thing is made exceeding light about the teller. The ftool is fixed to each chair with ftraps and but^ tons, and the whole thus finiflied produces, a pleafing appear- ance* Of the Librdry Cafe. Plate III. of the Appendix. The elliptic breaks of this bookcafe will produce a good efFe6l in the whole. The doors in the upper part' are intended to have fluted green lilk behind, and a drapery at top. The pilafters are. fuppofed to be glued to the flile of the door, and are hinged as in common. The. lower middle part contains clothes-prefs flielves, and every other part may be fitted up for books ; or the lower ellip- tic ( 8 ) tic breaks qaay be formed into a neft of drawers, as there is depth enough. The half cohimns on the lower doors are glued to the ftile, and the doors hinged as in common ; but for the fake of fliew- ing the defign to advantage, the open door is drawn as if the columns were feparate. The young workman fliould obferve, that the whole is to be made in fix carcafes, and fcrewed together, and then the plinth fliould be made to fit it, of one entire frame, and fcrewed down on to the carcafes ; as as alfo is the cornice and its freeze. Of the Pier tables. Plate IV. As pier tables are merely for ornament under a glafs, they are generally made very light, and the ftyle of finifliing them is rich and elegant. Sometimes the tops are folid marble, but moft commonly veneered in rich fatin, or other valuable wood, with a crofs-band on the outfide, a border about two inches richly japanned, and a narrow crofs-band beyond it, to go all round. The frames are commonly gold, or white and burnifh- ed gold. Stretching-rails have of late been introduced to thefe 8 tables, jiTss. /»?./. Pier Ty-yjiLES rfhfrok-n.Jr/. fu/'/ifh/h/ L '''—ry.M7rch.iy. 1703. fiTerr,/S,;,//l '7 J^S^. ///. 2. i,:lBKAl^'Y .'STEP^ .*1-Ta.BLE, /,/,-; 'JlTA'r'a-inn. ae. jUU/yti^ fi.rtrry.A/i'nJp ( 9 ) tables, and it muft be owned that it is with good effect, as they take off the long appearance of the legs, and make the under part appear more furnifhed ; befides they afford an opportunity of fixing a vafe or bafket of flowers, which, with their re- fle<5lion when there is a glafs behind, produce a brilliant ap- pearance. Some, in place of a ftretcher, have a thin marble flielf, with a brafs rim round it, fupported by a light frame ; in which cafe the top ought to be of marble alfo. Of the Library Steps and Table. Plate V. This defign was taken from Heps that have been made by Mr. Campbell, Uphollterer to the Prince of Wales. They were firft made for the King, and highly approved of by him, as every way anfwering the intended purpofe. There are other kinds of library fteps which I have feen, made by other perfons, but, in my opinion, thefe muft have the decided preference, both as to fimplicity and firmnefs when they are fet up. The fteps may be put up in half a minute, and the whole may be taken down and enclofed within the table frame in about the fame time. The table, when enclofed, ferves as a library table, and has a rifing flap, fupported by a horfe, to write on. The C fize ( 10 ) fize of the table is three feet ten inches long, thirty-three inches high, and two feet one inch in width. When the fteps are out they rife thirty-three inches perpendicular from the top of the table frame, and the whole height of the laft ftep is five feet five perpendicular from the ground. The perpendicular height of the hand-rail is three feet one inch above the laft ftep ; and obferve, that on o-, which is iron, is fixed a fmall flap on which a book may reft, fo that a gentleman, when he is looking at any book in his library, may note down a pafTage from it with- out the trouble of going down again. The method of folding the whole up is as follows : The triangular iron bracket g is unlocked by a catch which keeps it firm to the hand-rail, and the defk-flap fixed to it being turned over to the infide, the whole comes for- ward, and lies level upon the upper fteps. The ftandard Z* may then be raifed out of its focket, and, having a joint at the top, it turns up to d, as fliewn by the dotted curve line. The fliort ftandard <:/ ^ is then, by relieving a fpring, prefTed down below the edge of the table-top ; and the hand- rail and ftandard If having been folded together, as mentioned before, they both reft on the iron focket faftened to the front edge of the upper fteps. The horfe o is folded by the fide of the upper fteps, and then both they and the horfe fall down within the table frame ; and it muft be obferved, that in fold- ing ( II ) ing down the fteps, the hand-rail and ftandard, which refted for a while on the focket' faftened to the front of the fteps, fall into another focket of the fame kind faftened to the under fide of the table top, where they remain, and fall within the table frame when the top is folded down. Laftly, the lower fteps-^J are turned up to a horizontal polltion, and being hinged tc !^^ Aider which runs in a groove, the whole flips in as a drawer, and is enclofed by the flap/>, which turns up and appears as the front of a drawer. Of the Drazving-room Chairs. Plate VI. The frame of the right-hand chair is intended to be finiflied in burnifhed gold, and the feat and back covered with printed filk. In the front rail is a tablet, with a little carving in its pan- nel. The legs and ftumps have twifted flutes and fillets, done in the turning, which produce a good effe6t in the gold. The chair on the left may be finiflied in japan painting, in- terfperfed with a little gilding in different parts of the banifter, which has a lively effedl. The covering of the feat is of printed 4 chintz, ( la ) chintz, which may now be had of various patterns on purpofe for chair-feats, together with borders to fuit them. Of the Bidet Drejfing-Table, and Night-fable Bafon-Stand.. Plate VII. The drefling-table has a real drawer under the cupboard part, and the reft are fham. The right-hand cupboard door opens by a fpring-catch communicated to the patera handle in the center. The water- bottle is fupported by a round box, made of very thin wood, glued and canvaffed over to ftrengthen it, and fixed to the top. The bidet legs turn up with a joint. The defign fliews only legs at one end, but the other legs are fuppofed to be fold- ed up till the whole is taken out ; and when ufed, the legs are kept to their place by iron hooks and eyes. The fcale fhews the fize of the front, and its depth from front to back is lixteen inches and a half. The frame, to which the glafs is hinged, is fourteen inches in width. The night-table requires no explanation, and I fhall only obferve, that the covers with rings on them are meant for a tooth- "•1. ■<~--<i ■•^.:: ( 13 ) a tooth-brufli, and the ivory boxes on the right for tooth- powder. The fcale for the dreffing-table fliews the fize of the night- table, applied to the front, and its depth from front to back is eighteen inches. Of the Wardrobe. Plate VIII. The upper middle part contains fix or feven clothes prefs fhelves, generally made about fix, or fix inches and an half deep, with green baize tacked to the infide of the front to cover the clothes with. The lower part confifts of real drawers. The wings have each of them arms, to hang clothes on, made of beech, with a fwivel in their center, which flips on to an iron rod fixed by plates fcrewed on to each fide of the wings, as ex- preffed in the defign. The whole is made in four feparate carcafes. The wings by themfelves, and the upper and lower middle parts feparate. The plinth is made all in one frame, and likewife the cor- nice with its freeze, and being fcrewed to each carcafs, the whole is kept firm. D Obferve, ( 14 ) Obferve, that in the wings a bead is put up for the doors to fall againfk when they are fliut to ; by which means are cleared the knuckles of the hinges on the doors of the middle part. It fliould alfo be obferved, that as the furbafe cannot go round the out ends of each wing on account of opening the doors, the moulding is returned againft the front of each door. The furbafe on the middle part returns, and flops againft the inner end of the wing ; and the edge of the door of each M'ing, with the furbafe which is on them, are fcribed on to the aforefaid return, which then appears as an internal miter, and gives place to the opening of the door. The fcale, applied to the middle part, gives its height and length. The wings are two feet, and fixteen or feventeen inches deep; and the depth of the middle part about twenty-three inches. Of the Bed. Plate IX. This defign requires no explanation, except that which re- lates to the tefter. The cove of the tefter is to be formed by 8 ribs ; 17.V7. p/.:i A B 3<1 S I ©N foT A B E 15 , J'l.O. I ' ' '~^ 2 /,^^/ JT S^ur^n J^7. *>'*■• >:»i^. njU/jhfJ .IS //'f .lrf,fi/f,-f.t (,r I'r.'Jh-ri^ — J/m' iii.r~c;3. ( 15 ) ribs; one at each miter, and other fliort ones joined to them, with the reft about five inches apart from each other. At the upper part of the cove is a fqnare tefter into which the ribs are fixed. On the edge of this tefter, which is made very fight, is fixed a fmall moulding mitered all round. The cove being formed, the ribs may be covered with ftrong board-paper, both infide and out, which may either be japanned to match the fur- niture, or it may be covered with the furniture itfelf. The cir- cular part about the cove is nothing more than a ftraight board fixed on to the upper tefter. For the fake of eafy conveyance, the cove may. be made in four parts, mitering at each corner, and the ornament intended to be at each miter on the outfide running entirely up to the feathers, will hide the joint. The fwags of filk line that appear on the drapery fhould be faftened to the back part of the cornice, in order that they may hang eafy. The pillars are to be japanned. The pannel that hides the fcrews is made to flip into a groove at the bottom, and being bevelled off behind at the top, when raifed up a little from their place, by prefting the finger on the front, can eafily be taken away to come at the fcrews. The valence and drapery both together flip on to a lath as in common. Of ( i6 ) Of the Sofa and Converfation Chairs. Plate X. With refped: to this fofa, all that is neceffary to be ob- ferved is, that in the fpace between the divifions of the back part, it is meant that there fhould be a ground-work covered with lilk, to fuit the reft of the fofa. Againft this ground the two columns and the ornament are fuppofed to reft. The converfation chairs are iifed in library or drawing- rooms. The parties who converfe with each other fit with their legs acrofs the feat, and reft their arms on the top rail, which, for this purpofe, is made about three inches and an half wide, fluffed and covered. For the convenience of fitting in the manner juft men- tioned, the chair is made long between front and back, and very narrow at the back and front in proportion. The height of the chair to the fluffing is three feet ; at the back ten inches, fpreading out in width to the top rail, which is twenty inches in length. The front is fixteen inches, and the height of the feat as in common. Of AZ^i.-i. />/. /■ A Sofa P!./0. r v/,, ..,,/„„ /J, /'ti/'/r.i/i,,/ ,/.y M/ JiV M/'Yi/s /;/ Cr.Tcriy— .Ifiii/ /,■ i~ij.-,. ^ ^1 u H ;' X X ^ ^ «5 ••i I 5* .V'li.T. />/.:{. /'/' A !Lijbiix\ry Table Willi Si^^CRETAtiwBRAWER .3 ?'^/„// /,/„„ \ / r.w^„,/,;-.,/-/ rutt,//,J li/ &y?rr-l/ ~Jtiii/y,f^ip. frjfny ■ ^M ( 17 ) Of the Card Tables, Plate XL On thefe tables it is fcarcely necellary to fay any thing, cfpecially as the quarter plans fliew how they mull be framed ; and therefore I fliall only obferve, that the ornaments may be japanned on the frames and carved in the legs. As to the me- thod of managing the tops, I take it to be the beft to rip up dry deal, or faulty mahogany, into four inch widths, and joint them up. It matters not whether the pieces are whole lengths pro- vided the jump-joints be croffed. Some tongue the jump-joints for flrength. After the tops are dry, hard mahogany is tongued into the ends of the deal, then flips are glued on the front and back, that the whole may appear folid mahogany, if a moulding is to be worked on the edge ; but if the edge be crofs-banded, there is in this cafe no need for tonguing in mahogany. ■Of the Library Table iviih a Writing Drawer. Plate XII. This table is intended either to lit or Hand and write at. The height of the fecretary drawer is adjufted for fitting, and £ the ( 18 ) the top of the table is high enough to ftantl and write on, efpe- cially if the middle top be raifed by a horfe, as fliewn in the de- iign. This table will alfo prove very ufcful to draw on ; for when the middle part is up for drawing upon, there remains fufficicnt room at each end of the table on which to place the neceflary imj^lements for drawing ; befides, the drawers at each end may be fitted up to hold colours of various kinds ; I mean the two upper ones, for there are drawers quite down to the plinth. The drawers under the fecretary will hold the large flicets of drawing paper, together with the tee fquares ; and as it will not be neceflary to make the drawers under the fecretary the entire width of the table, the oppofite front being made fliam to have the fame appearance, the whole of it may be hinged at bottom and locked at the top, and the infide will al- low depth for books. This fliam front being a confiderable width, it would hazard the hinges to let it reft wholly on them when turned down, and therefore there fhould be iron rule- joints at each end as ftays. To thefe conveniences there are alfo four cupboards en- clofed with doors, as fhewn in the defign ; and the whole finifli- ed in this manner, I venture to affirm, will prove as ufeful a table as has ever been devifetl or publiflied. In ( 19 ) In refpe<5l to the manufadluring part, it will be bed to make it in two parts. The upper part containing the fecretary, and two drawers at each end ; and the lower part, four drawers under the fecretary, a book- cafe behind, and four drawers at each end, the lovvermoft of which is iliewn in the defign. The top (liould be framed of inch and quarter wainfcot (as defcrib- ed in page 373), containing a well for the defk part, which may be made to rife on the front as well as at the back, by forming a double horfe ; but in this defign it is only intended to rife at the back by a fmgle horfe, and hinged to the crofs- band at the front. The cupboard doors may either be framed and pannelled, or glued up to their fwegp in narrow flips of inch mahogany, and clamped ; not by tonguing, but by a fquare joint, and pins driven through the clamps. The management of the circular bafe-moulding and plinth may be learned in page 375. Of the Fire Screens. Plate XIIL The lyre fcreen is conftrucSled upon an entire new plan, it being defigned to turn upon a fwivel, which fixes to the vafe and ( 20 ) and paflcs through the bottom rail, fo that the fkreen may be twrned to any pofition without moving the Hand. The fcreen part, which rifes between the ftandards or pil- lars, is fufpended by a weight in the taffels, which are commu- nicated to the fcreen by a hne pafling through the pillars and over a pulley fixed to their top. There muft be a dovetail groove in each ftandard, and the fcreen made to fit into thefe ; fo that the ftandards may keep their proper place, and not fly open at the tojj. Obferve, that the ornament on the tops of the pillars or ftandards rife up with the fcreen, being fixed to it, and detached from the pillars. It is intended that the lyre ornament be carved in has relief, gik and burniflied ; which, when planted on to a blue filk or fatin ground, cannot fail to produce a fine efFedt. The other fcreen being common, needs no explanation, only that it is fufpended by little fprings fixed in the dovetail grooves of the ftandards. Jn A. Cabinet /^ TS/„;nt!:>,.M. jPuili/hdh/TSAeratoHMi/. 'h '. /^.V, ( 21 ) In refpedt to the general fize of horfe fire-fcreens, about eighteen inches or nineteen may be allowed for the breadth, and three feet fix or feven inches for their height. Of the Cabinet. Plate XIV. This cabinet, I prefume, is as new as the fire-fcreen, ana will have a better effedt in the execution than in the defign. The front of the cabinet is hinged to a Aiding piece which runs in a groove, upon the fame principle as the writing-table page 408. The front being turned down to a horizontal poii- tion, it may then be flipped in till it flops. To fupport the front thus turned down, there are two Aiders which come out of the plinth on which the cabinet refls. Thefe fliders come out by relieving a fpring which is fixed in their fide, and having a common fpring behind, they are forced out fo that the fingers may lay hold to draw them quite out. They are lined with green cloth both at top and bottom to prevent them from fcratching both the front and top of the cabinet. The infide of the front is alfo lined with green cloth to write on. The infide of the cabinet is fitted up in the manner fliewn in the cabinet, Plate XVI. F Above ( ^2 > Above the falling front is a drawer, to the under fide of which the front locks, fo that the drawer and front are either locked or opened at one time. Above the drawer is an ornamented freeze, japanned ; and round the top, which is marble, is a brafs edging. The flower-pot at the top and that on the ftretcher are fup- pofed to be real, not carved. The columns Itan^ clear, as Ihewn by the plan ; and they are intended to have brafs bafes and capitals, with wooden. Ihafts fluted. The candle branches turn to any form in a focket, and the whole may be taken away, as they are only fcrewed into a nut fixed into the legs of the table.^ There is a brafs fret fixed at each end, which finiflies at the llandards of the candle-branches. The lower frame contains a drawer in front, and the legs being odtagon, are intended to be veneered croff'ways as far as to the carving, which may be gilt to fuit the bafes and caps of the columns. 0/ Dressing Chests JVy.36'. />?..-i. P/. AT. /; sA.-f :*/.•■■ / /■„/,/rJ„./ „, f/,, .1.:' />;r.;-/., /,,, t; Ji, f ( 23 ) Of the Dreffing Chejls, Plate XV. These chefts are alfo on a new plan, particularly as the common Aider generally ufed for merely writing on is turned into a fhallow drawer, which contains a little writing flap which rifes beliind by a horfe, and places for ink, fand, and pens, and alfa drefling-boxes. When the drawer is in, it appears like a common Aider, with a partition above and below, as that with the convex front. There is therefore no flip under the top, as the drawer fldes mufl: run clofe up to it. The drawer below of courfe mufi; lock up into the under edge of the drefling-drawer, and the drefling-drawer into the top, which is done at one time, by the bolt of the under lock forcing up that of the upper one. The height of thefe chefts are always governed by the Aider, which runs thirty-two or thirty-three inches from the floor. The fcale fliews their length, and their breadth is twenty-two or twenty-three inches^ 0/ the Lady's Cabinet, Plate XVI. The cabinet in Plate XFV. is made in two parts, but this is entirely in one. The legs and columns are therefore all in one piece. ( 24 ) piece. The infide of the cabinet is made feparate, and (lips in between the legs, and a piece of narrow wood, as a band, is fit- ted to fill the fpace up to the column, as the defign fliews. The marble flielves, with frets at each end, are for a tea equipage. Above and below thefe flielves are drawers which turn out by a hinge. Above and below the front are alfo draw- ers. The drawer below may be made to fupport the front when turned down to write on, or it may be fupported by brafs joints, as fliewn in the defign for the infide of the cabinet. The fcales and plans of each cabinet fliew their length and breadth ; it remains only to mention their height, which is four feet, and four feet two. Of the Horfe Drejfing Glqfes. Plate XVII. The dreflTmg-glafs on the left rifes to any height, by leaden -weights inclofed in the ftandards. The weights are fufpended fometimes to tambour glued on to webbing, which pafles over a brafs roller at the top, and fixes to a piece of thin wood, tam- boured to match it. Through this piece of thin wood is put an iron pin, with a thin plate to it to fcrew it faft ; which pin goes through the fide of the glafs, and fallens by a nut at the infide, fo ( 2.5 ) fo that when the glafs is raifed, it may be turned to any direct tion. But fome ufe a kind of coloured llrong webbing, without the tambour, which makes it lefs troublefome, and lefs Hablc to injury, though it does not look fo neat. Thofe unacquainted with the manner of gluing up the ftandards, may fee a fediou of them in Plate XXX. Fig. C. There is a brafs handle behind the ornamented top to raife the glafs by. The boxes on each fide arc intended to hold conveniences for dreffing. On thefe, there is a comb-tray on the left fide, and a pin-cufliion on the right. When the drefling-boxes arc not in ufe, they are intended to turn behind the glafs. For this purpofe they are fixed to a brafs focket, which turns upon a fliort brafs rod, and by a fcrew they may be raifed up or Ionv- cred at pleafure. See Fig. D. Plate XXX. The other drefiing-glafs has a convenience for writing as well as for dreffing, which convenience rifes by a little horfe. The dreffing-boxes are made with clofe covers, and a llider in- clofes the whole, fo that when the whole is turned up nothing can come out of its place. The glafs does not rife as the other, but fixes in centers, fo as to move in any pofition either back or forward. G And ( ^-6 ) And obferve, that when the dieffing-flap is turned up it locks into the toj^ rail, and the glafs of eoiirfe falls to its own place. The under fide of the flap being the front when turned up, it may be japanned and banded. The lower parts of the ftandards are fliapcd Uke a lyre ; and to form the ftrings, braf& wire is let in, wliich has a pretty effecft. Of the Charfe Longus. Plate XVIII. ^" These have their name from the French, which imports a long chair. Their ufe is to reft or loll upon after dinner, and in fome cafes the lower one will ferve for a fofa. The drapery under the rail is tacked to a rabbet left on purpofe. The upper one is framed firft in two parts. The end, or chair part, is made to receive the ftool part within its lides ; and the fides of the ftool part fcrew in againft the infide of the chair. As to any other particular, the defigns themfelves are fufficient to point them out. Of the Engli/h State Bed. Plate XIX. In giving a defign for an Englilh ftate-bed, or fuch an one as is fuitable to the dignity of a prince, and worthy the notice of a king, I conceived it neceffary to cultivate as much as I could I - the ^^37- Pf-s Chaise Loxches /'/ni /:t!/jt/iJ /y tijirry - J<uif -Af, iy,p ^7j'rrtiSri///i . A^^ English Statk r>Ki»' // /,! //;,//.,.////'-."/ „'./,,/„.- ,,, d. ./,//, -, ,.„ ,. C 37 ) the moll exalted ideas, unfettered and unreftrained with the thoughts of expenfivenefs, which naturally produces meannefs of compolltion, and in many cafes injures the ingenious in their defigns. For ornament to a bed of this kind, it ftruck me that no- thing could be more fuitable and charadleriftic than fuch as ex- prefled fymbolically the different parts of our government, to- gether with thofe virtues and principles which ought to be the fupport of regal authority, and the ruling maxims of every good government of whatever kind, whether monarchical, ariftocrati- cal, or democratical. Emblems of war have been avoided as much as poffible, being inconfiftent ornaments for a bed, and becaufe good kings ought not to delight in war, but in peace, unity, and the love of men and their fubjefls. As our government is compofed of three diftindl branches, the figure on the right hand bed-piUar is intended to reprefent the democratic part of it, or the power of the people invefted in their reprefentatives in parliament. In iconology :'■, democracy t is reprefented by the figure of * Iconology, from uwv, eikcn, an image ; and xiya, lego, I fpeak. The interpretation of ancient images, monuments, and emblems. t Democracy, from /n/uoj, detnos, people; and xf*Tf;v, kratein, to command or govern; is when the Ibvereign power is lodged in the body of the people. a woman ( 28 ) a woman dreffed in a homely garment, and crowned with vine leaves. In her right hand Die holds a pomegranate, which de- notes affemblies of the people on matters of importance. In her left hand is a clufter of ferpents, which expreffes the winding and flow progrefllon of democratic ftates, owing to the inability of the common people to govern. Her ftanding on the two facks of corn which reft on the pedeftal, flgnifies that democratic go- vernment is more attentive to the obtaining of neceflary pro- vifions, than the increafe of fame, or the acquifition of honours. If this be a juft reprefentation, and founded on fa<5t, the reader will, no doubt, confider the democratic branch a very important one, and for which reafon it is here placed near the ground- work. The figure, oppofite, on the left pillar, reprefents the ari- ftocratic branch. Ariftocracy* is defcribed by the figure of an elderly lady, in a fumptuous drefs, with a crown of gold upon her head. Painters reprefent her fitting on a throne ; M^hich is a pofition confonant to lawgivers, but which I could not make fuitable to this fituation. In her right hand flie holds the con- fular fafces, that is, a number of elm rods tied in a bundle, with a hatchet in the middle, which, originally, were the enfigns of * Ariftocracy, from aj ij-O;', ari/Ios, the beft ; and xjanx, iratlo, T command or govern ; ks when the fupreme power is lodged in a fenate, compofed of the principal perfons of a flate, .either for their nobility, capacity, or probity. fovereign ( 29 ) fovereign dignity, but in after times the hatchet was taken out, and they were carried before the confuls or magiftrates of Rome, to denote their authority. Thefe rods are entwined with a crown of laurels, a fymbol of reward due to thofe who have maintained the public welfare, and have performed great ac- tions for the good of the ftate. In her left hand is a fteel cap, at her feet a hatchet, a plate, and purfe with money, all which denote that arms and finances are necefiary fupports of ftates. And I would here obferve, that it is not abfolutely neceffary to confider the fteel cap and hatchet as fymbols of war, but of the executive power requifite in all governments for the mainte- nance of peace, and the punifliment of evil doers. The figure in the center of the upper cornice is intended to reprefent the monarchical branch of our government. Monarchy- is characterized by the figure of a young wo- man of grave countenance, feated on a terrertrial globe, holding four fcepters, to denote dominion and power. The other hand being uplifted, denotes her authority in giving command. The rays of light furrounding her head, denote luftre, and the re- fpeft due to her greatnefs. The lion on each fide fymbolizes the * Monarchy, from ^tvss, monos, alone; and a?^:., arche, government i is when tho fupreme power is inverted in one pcrfon, commonly termed the King. H power C 30 ) power which ihe poITelTes and requires of others in order to her fupport. Painters, however, defcribe her with trophies of war, and a crowned head chained down as a captive at her feet, which I have here omitted, hoping that conqueft and war are not the prominent features in our government. Thefe three figures in their fituation to each other form a triangle, whofe bafe is democracy and ariflocracy, and whofe fummit is monarchy; denoting that monarchical power and ho- nour are originally derived from the people, and that without their fupport, monarchy in its moll exalted ftate muft fall. The lions which fupport the bed, with oak foliage and leaves on the bed-frame and round the fliafts of each pillar, are emblems of the ftrength and permanent nature of our govern- ment. The acorns being the fruit of the oak, denote, that by long progreffive improvements it is arrived to a good degree of maturity. The ferpents in the cornice, which mutually entwine them- felves round Mercury's rod, denote the unity, prudence, and wifdom, requifite to monarchs in the exercife of their impor- tant charge. The trumpets and laurel crown are expreflive of the fame which the Englifli ftate has acquired through the mildnefs of its government. The beads under the cornice de- note ( 31 ) note its riches. The bafkets of fruit on each capital, and in the quadrantal pannels, fymboHze the profperous ftate of the na- tion, and the plenty we enjoy, hi the arch of each quadrant are marked the degrees, to denote that navigation has contri- buted greatly to our riches and fafety. The lyre and trumpets on the pedell:al above the cap, fignify the flourishing ilate of the arts ; and the fpreading oak leaves and rofes, are meant to exprefs the defigner's willi and hopes, that the ufeful arts may long continue to grow and fpread themfelvcs under the muni- licence of our government. The coronets round the dome are thofe of the immediate fons and daughters of the king of Great Britain, of which there are thirteen; but the dome being divided into fixteen compart- ments, itill leaves room for an increafe of the royal family, to denote that the fubjedts of Great Britain fhould hope for a long fucceffion of a mild and good government. The feftoons of flowers denote that happinefs and prolperity are wifhed to fur- round each branch of the royal off'spring. The crown of England is fupported on the top of the dome by three figures, intended to reprefent Juftice, Clemency, and Liberty; for notwithftinding thefe may, in fome. inftances, be fiillied in our government, yet fcarcely any nation can boalt of pnore than that which we have long enjoyed. 8 Juftice, ( 32 ) Juftice, which ought to be the moving principle of civil government, is by painters defcribed by the figure of a woman drelTed in white robes ; holding in her left hand a fword, to pu- nifli criminals ; and in her right a pair of fcales, to give that which is due to every one without partiality ; which imparti- ality is denoted by a bandage over her eyes. In this fituation the fword and fcales may be fuppofed to lie on the other fide of the dome ready for ufe. Clemency is a necefTaiy quality or principle in government, by which thofe in authority are enabled to take into confidera- tidn, and to effedt the relief of the miferies of the helplefs and infolvent. hi the exercife of this virtue, he who is ready to be ent afunder by the uplifted hand of juflice can be faved, and the rotting infolvent prifoner can be abfolved and releafed. Such adtions beget gratitude in the minds of the fubje<fts, and are as a pillar to the crown ; while cruelty and tyranny have of- ten proved fatal to princes. . "ici J. I. Painters defcribe this virtue by the figure of a woman crowned with olives, as a mark of her peaceful and gentle tem- per ; and drelTed in a purple robe, which denotes her eminence. She is chara6terifed by the mildnefs of her countenance, and fitting on a lion (which I could not here introduce). She alfo holds a laurel branch of honour and refpedl in her right hand. She ( 33 ) She is faid to have a fpear by her fide, fo that when her mercy is abufed fhe may in juflice revenge it. The other figure, Liberty, on the other fide of the dome, is an eflential principle to good government. It fuppofes a difpo- fition in thofe polfeffing fupreme authority to allow fubjedls to enjoy their natural, moral, and religious rights. In the polfef- fion of thefe we are delivered from flavery ; the yoke is broken. Therefore painters reprefent liberty by the figure of a woman, with a broken yoke-ftick in her left hand, and trampling upon it as a mark of refentment. She is dreflTed in white robes, to denote the bleffings which flie confers on mankind; and in her right hand flie holds a fceptre as a fign of independence. She has alfo a cap of liberty on her head, in allufion to the cuftom of the Romans, in fetting their flaves free ; who alfo fhaved their heads, and permitted them to be covered in the prefence of thofe who gave them liberty *■, The figures on the other fide, and at the end of the bed, may be the fame, not merely for uniformity's fake, but to convey the fentiment exprefled by the allegory with more weight, as it is well known that repetition is fome- * Ricbardfon's Iconolqgy, from whofe work I am indebted for feveral ideas on this fubjeft, I times ( 34 ) times, introduced to give force and energy to a fubjecfl. How- ever, if any fliould think it n^ceffary to vary the figures on. the different fides, there are plenty of fubje6ts fuitable enough. Fortitude may be placed on the center of the cornice, oppo- iite to monarchy ; to denote a quality of mind fo highly necef- fary in thofe who rule. The emblem of this quality is a wo- man refting on the fhaft of a column and its bafe, having a brown robe and part of a military drefs, with a lion on one fide of her ; but flie may have one at each fide, to make the outline more agreeable to the figvire of monarchy. Her militaiy drefs conveys the idea of courage; and refting on a column, fteadinefs and firmnefs ; and the lion, ftrength of mind. On the bed pillar, oppofite to the figure which reprefents the ariftocratic branch of our government,, fiiould be Counfel, to denote the wifdom and ability necefl*ary in thofe Avho make up that branch. Counfel is reprefented by the figure of a grave old man, having a long beard, drefled in long robes of violet colour. His age denotes that experience requires length of time, and that wifdom. is the refult of experience. His long robes denote his ( 35 ) his high chara<^er, and their colour his gravity. He is repre- fenfed fitting, to (liew his authority; and with a chain of gold round his neck, to which is fufpended' a human heart, to denote his integrity. In his right hand is a book, to Ihew he has re- gard to law, and that from literature he obtains his knowledge. He may, however, in this fituation be Handing, as the bed-pillar will not fo well admit of a fitting attitude ;- and in this attitude he may have a mirror in his left hand, furrounded with fer- pents, to denote prudence and fpeculation, as neceffary to good counfel. « On the other pillar, oppofite to the figure which reprefents the democratic branch of our government, there may be the emblem of Law, to denote that the members of parliament, as the reprefentatives of the people, ought to be acquainted with the rights and interefts of their conftituents ; and alfo, that in their debates on thefe fubjed:s, they ought to regard the laws of the conftitution. Law is reprefented by the figure of a refpeaable elderly lady, fitting on a tribunal chair. Her age denotes that law is an ancient fubjea ; flie is feated to denote eminence, and hold^ a fceptre in her right hand to denote authority. In her left hand fhe holds an imperial crown allufive to the law of nations, importing ( 36 ) importing that no nation can exift without laws. Her head is adorned with diamonds, to fignify that law is moft precious, and that its origin was from God. At the end of the bed, and next to law, Obedience or Sub- jedlion may be introduced, to denote the duty and refpe6t which the people owe to their reprefentatives whom they have ap- pointed, and particularly to fignify that fubjeds ought not to rebel againft government. Obedience is defcribed by the figure of a humble woman, in an upright pofition, with her eyes towards heaven, to denote her regard to its commands as the Appointer of government. Her upright pofition not only fhews her wdllingnefs to obey, but that government was never appointed to opprefs or bow down the backs of thofe who are willing to obey juft laws. She is dreffed in white robes, denoting innocence ; and acrofs her fhoulders is a yoke, the emblem of patience and obedience. By her fide may be reprefented a dog, which is a fymbol of obedi- ence and faith fulnefs. On the center of the cornice may be reprefented Authority, to denote that without its influence law is rejected and con- temned, — obedience is without foundation, and therefore go- vernment could not exift. 8 Authoritv ( 37 ) Authority is reprefented by the figure of a matron, or old lady, to fliew that the inftitution of authority which gives ef- fect to laws is ancient as law itfelf. She is feated on a regal chair, becaufe princes and inagiflrates generally perform their office fitting, indicating tranquillity of mind. She holds a fcep- tre in her left hand, denoting regal power and authority ; and by her fide are arms, to fignify her power to punifli the licen- tious, and protedl the obedient. In her right hand is a book, refting on her knee, to denote that civil authority is of divine origin*. On the other pillar may be the reprefentation of Tyranny chained down, with her back bowed, to fignify that thofe in. authority ought to fupprefs rather than cherifli it ; and to fliew that tyranny ought, in all good governments, to be at the foot of power, to prevent its baneful effe<Sls in a ftate. The em- blem of this noxious quality is a pale, proud, and cruel-looking woman, drefled in armour, and purple drapery, to denote her readinefs to llied blood in the defence of her arbitrary meafures. In her left hand is a yoke, and in her right an uplifted fword, to fliew that flie is ready to enflave mankind, and punifli them if they will not put on the yoke. She wears an iron crown, to * See Rom. xiii. i. — Not indeed for the purpofe of enflaving mankind, but to be a terror to evil-doers, and a praiCe of them that do well. Nor is the candid reader of this defcription to imagine, that the writer has even the moil diftant view of maintaining hereditary right of fuccefiion as facred, but only that civi) government itfelf, of whatever kind, is of divine origin, and ought therefore to be revered by every wife man. K flicw ( 38 ) Ihew that the authority which tyrants feek is for bafe purpofcs and cruelty. To make thefe three figures harmonize — Authority, at the top of the cornice, may be reprefented as looking towards Obe- dience with an eye of approbation ; and the book lying on her lap, w ith the right hand flie may hold a dart pointed dire<ftly to Tyranny below. And to reprefent Tyranny in the moft wretched Hate, her iron crown may appear to tumble off her head, her yoke broken, and her fword pointed to her own breall, to fliew that in the end tyranny is her own executioner. Thus, I think, the end of the bed wall exhibit emblematically the defign of civil government, which is to protedl the innocent and obedient, to fupprefs cruelty and oppreffion, which are the life and foul of tyranny. The fi-ont fide fliews the nature of our government, the dome the principles which fupport it, and the back fide the way in which government is managed. The ornaments on the head-board are emblems of love and continency, exprefled by the figure of Cupid, Chafl:ity, and a trophy below. Cupid is reprefented as drawing his bow to guard Chaftity from tlie violent attempts of Impurity, whofe figure, partly a woman and partly a monkey, is behind the cur- tain, to denote that fuch as praflife it lurk in fecret. The emblem of Chaftity is the figure of a young woman in white robes, to denote purity and innocence. Her head is 1 crowned ( 39 ) crowned with a garland of cinnamon, a pleafant and coftly plant to lignify- that Chaftity is a virtue both pleafant and valuable. She is veiled, to exprefs her modefty; and in her right hand holds a fceptre, as a fign of her conqueft over luft. In her left fhe holds a turtle dove,, which is an emblem of continence. With refpedl to the manufa6luring part of this bed, it fliould be obferved, that the curtains draw up by a pulley at the feveral corners, detached from the drapery valence which is fix- ed to the cornice^ The tefter on which the dome refts, is made perfectly ftraight, and forms an even furface on both fides ; which, in the infide, is pannelled out with gilt moulding, at each angle. The quadrantal pannels recede back from the cornice, and are framed into the top of the pillars, which are left fquare. The ground of thefe pannels being continued the whole length, from pillar to pillar, ferves as a facia on which to fix the cor- nice. Then obferve, that the bafket of fruit and the lyre being in one piece, they are fixed to the pillar, and meet in a miter with the other fide. The oak foliage is in one entire piece, and fcrewed up to the bed-fides, after the drapery valence is tacked to a rabbet made for that purpofe. Every ( 40 ) Every other paiticnlar muft naturally occur to the work- man, after what has already been faid on the other beds in this work. Upon the whole, though a bed of this kind is not likely to be executed according to this defign, except under the mu- nificence of a rayal order, yet I am not without hopes that ufe- ful ideas may be gathered from it, and applied to beds of a more general kind. Of the DreJJing Commode. Plate XX. With refpecfl: to the dreffing part of this commode, it may be made either fixed faft, or to be brought forward in the man- ner of a drawer, with leapers to keep it to its place. If it is made to be fixed faft, the doors may be opened to form the knee hole. The top which covers and enclofes the dreffing part, flides down behind, in the manner defcribed in page 407, to which I refer the reader ; only obferve, that in this top there are miters to fit the ftraight moulding in front when the top is put down. A bottle of water, and a pot to receive it when dirty, can both be kept in the cupboard part. The dreffing-table below can require no explanation, ex- cept what relates to the fize, which from front to back is eighteen ALABifS Bressiito Commobe, J'/.lia. iTJA^rainn de/tM /ii/^l^^if ,zjmf^^UimAf,l, r.M/r,jkm Jiiir z-ff^iy^s. ^rS^r^'H /'""^ $ ^ I" ( 41 ) eighteen inches, thirty-four the whole height, and two feet four the length of the front. Of the Sideboard^ with Vafe Knife-cafes. Plate. XXI. The pedeftal parts of this fideboard may be made feparate, and then fcrewed to the fideboard. The top extends the whole length in one entire piece, and is fcrewed down to the pedeftala. The hollow plinths of the vafes are worked in one length, and mitered round. The top of the plinth is then blocked on at the under fide, and the vafe part is made to fcrew into it fo that the vafes may occasionally be taken off. A crofs band is meant to be mitered all roimd the hollow plinths, coming forward to the edge of the top ; fo that if the top be veneered, it will only require the length between the two plinths. Within the front is a tambour cupboard, which is both ufeful, and has a good effedt in its appearance ; almoft any workman will know how to manage this, fo that I need not explain it. The ornament behind is brafs, intended as a flay to filver plate, and has branches for three lights. The circle in the center may have a glafs luftre hung within it, as an ornament. For any other particular relative to fideboards in general, fee page 363, where the com- mon principles of this ufeful piece of furniture are explained. L 0/ ( 43 ) Of the Library Steps. Plate XXII. The si: fleps are confiderably more fimple than thofe al- ready defcribed ; and though not fo generally ufeful, will come vaftly cheaper. The upper flight of fteps turn down upon the under ones, both of which rife up and Aide in as a drawer ; af- ter which a flap, which is Ihewn in the defign, is turned up,, and lias the appearance of a drawer front. Obferve, that the refting poll: at the top folds down to the fide of the fleps by means of an ii'on joint. The horfe has green cloth under its feet, to prevent its fcratching the top. The defign fhews that the two fteps are connected together by hinges, fo made as to clear the edge of the table-top ; and alfo, that there is a Aiding board to which the under flight is hinged, which fliding-board runs in a groove. The length of the table is three feet fix inches, its width twenty-two inches. The table is thirty inches high, the upper flight is thirty perpendicular, and the refting-poft thirty-three. This, and the other defign for library fteps, have obtained a patent ; yet any part being materially altered, will evade the adt, though the whole be nearly the fame. Thofe mafters, how- ever, who do not think it worth their while to be at the trouble of ( 43 ) of introducing any eflential alteration in them may have thefe fteps from Mr. Robert Campbell and Son, Mary-le-bone Street, London, with a fufficient allowance for felling them again. Of the Chamber Horfe^ The upper figure fhews the infide when the leather is off, which confilts of five wainfcot inch boards, clamped at the ends ; to which are fixed ftrong wire twilled round a block in regular gradation, fo that when the wire is comprefl^ed by the weight of thofe who exercife, each turn of it may clear itfelf and fall within each other. The top board is fluffed with hair as a chair feat, and the leather is fixed to each board with brafs nails, tacked all round. The leather at each end is cut in flits to give vent to the air, which would otherwife refifl the motion down- wards. The workman Ihould alfo obferve, that a wooden or iron pin is fixed at each end of the middle board, for the purpofe of guiding the whole feat as it plays up and down. This pin runs between the two upright pieces which are framed into the arms at each end, as the defign lliews. 4 The ( 44 ) The length of the horfe is twenty-nine inches, the width twenty, its height thirty-two. To the top of the foot board is eight inches, and to the board whereon the feat is fixed is thir- teen. Of the Comer Kigbt Tables. Plate XXIII. That on the right requires no explanation, except that the doors may be hinged to turn in, if it is thought moft con- venient. The table on the left is intended to anfwer the purpofe of a wafli-hand ftand occafionally. To anfwer this end the top part is framed together of itfelf, and fixed by an iron or ftrong wooden pin, into the back corner of the lower part, which con- tains a focket, fo that the top part can be turned to one fide, as Ihewn in the defign, or as much further as is necelTary to clear the hole. Obferve alfo, that on the front is worked a groove, in \vhich a pin paflTes that is fixed to the front of the bottom of the upper part, and prevents the top part from turning quite off from the "bottom, which would endanger the pin on which the top part turns; it lliould have caftors at the brackets, that when the night ( 45 ) night table is wanted, it may be drawn a little forward from the corner of the room to give place for turning round the upper part. It fliould be about thirty-four inches to the top of the bafon llielf. The height of the feat lixteen inches and a half, and its other dimenfions are known from the plan. The bottom drawer may be made neat, and drawn out by means of a dovetail groove in the middle of the drawer, and a piece to fit it fixed acrofs the bottom of the carcafe. Of the Pulpit. Plate XXIV. The defign of introducing a pulpit into this work was to afford fome affiftance to the cabinet-maker, who in the country is generally employed on fuch occafions. In eredling a pulpit of this kind, three particulars ought principally to be regarded. Firft, the plan ; fecondly, the manner of conduding the fieps and hand-rail round the column ; and, laftly, to fix the whole firm, fo that it may not by fiiaking produce a difagreeable fenfation to the preacher. The plan of this pulpit is a regular hexagon, which to me is th^ moil beautiful and compa6t of any. One of its fides is occupied by the door, and one for the back of the preacher, another to reft his arm, and the remaining three for the cufliion. M The ( 46 ) The plan of the fteps is a circle, which is moft convenient where there is a want of room. The plan fliould be divided according to the number of fteps necefiary for attaining to a proper height, which in this cafe is twelve, as one, two, three, &lc. in the plan. A feflion fliould then be drawn, and the height of the rifers adjufted to the number of the fleps, as in the fed:ion a, by c, 8cc. Draw the femi plan P, and divide the circumference into eight equal parts, as i, 2, 3, 4, Sec. becaufe, that in the plan there are fo many fteps contained in its femi. Draw from i, 2, 3, 4, 8cc. lines perpendicular, and continue them to the uppermoft fteps. From ^, the firft ftep, draw a line to a on the plan P. Do the fame from h xo h, c to c, and fo of all the others, which will defcribe the fteps and rifers as they re- volve on a cylinder. The face mould for the hand-rail, when it is cut out of the folid, is found as follows. See Plate XXX. Draw a quarter plan as there defcribed, divide the chord line into any number of equal parts, as i, 3, 5; from which raife perpendiculars to interfe<Sl the circumference; draw next the rake or pitch-board of the fteps at Fig. R. by taking the breadth of the ftep on the plan, and repeating it i, 2, 3, 4 ; then take 7 the ( 47 ) the height of four rifers, as from x to /, and draw the Hne y 4, ^vhich line will be the chord for the face mould; therefore take y 4, and divide it into fix, as in the plan of the hand-rail. Take the perpendicular heights as i 2, 3 4, and 5 6, of the plan, and transfer them to the correfpondent perpendiculars on the face mould, which will give points through which the curve is to pafs, to form the face mould, as the figure fhews. Three of thefe lengths will be wanted to complete the hand- rail, including the ramp and knee. Thefe hand-rails are however fometimes glued up in thin pieces round a cyhnder in one entire length, after which a crofs banding is put on the top, and rounded off. In this cafe a cy- hnder is formed in deal, and the line of the fteps is traced out as defcribed Plate XXIV. which is the guide for the thin maho- gany to be bent round. In fixing the fteps, I prefume it will be found the beft method to mortice and dovetail the rifers of each ftep into the pillar : this may be done by making the mor- tice as much wider than the breadth of the rifer as the dovetail is intended to be in depth, fo that when the rifer is put into the mortice, it may be forced up to its place by a wedge driven in at the under edge of the rifer. By this means it will be impof- fible that the fteps ftiould work when they are tongued and blocked together. The foffits of the fteps are in the form of an 'r Ogee, ( 48 ) ogee, aiifwerable to the brackets, and are fitted up feparately af- terwards. ' In fixing the pillar it muft be noticed, that it is firfl te- noned into tranfverfe pieces of oak timber, which are funk a good depth into the ground, fo that when the clay is beat in folidly about the pillar it cannot work ; yet it is eafy to conceive, that in the pulpit it will be liable to fpring when the preacher is in it ; to prevent which I have introduced a light fmall co- lumn, fituated in the center of the pulpit, and connected with it by a cove, on which the pulpit rcfts. The found board is made as light as pofiible, which finiflies in an odlave cove at the top, and is fixed to the pillar by a ibong fcrew and nut, together with a tenon, which is funk into the found board. The bannif- ters of the hand-rail may be llraight bars of brafs, made very light, dovetailed into the ends of the fteps, and let into a plate of thill iron at top, which is fcrewed to the under fide of the hand-rail. Obferve, that on the left fide of the plate is a fcale of feet and inches, from which the various meafurements may be taken. N. B. Plates 25 and 27, 28 and 29, require no explanations ; ' they are therefore omitted. ■iVyjy. pi. 3- A^'l ~T\ rS*frm/tn J^ A I'l'Li'ir 7'M/>,i//y fi-Tirry.- Jh., '// I^^M. S-3f rr-y Jet^ . o Hi O H o o t^ Or ' ;^tep= ""'^ ^^ i 1 1 ! i ^ ^.. ]J f K •^"'T-Tn'^ i._ "~1W1IPI!I:I!I;'W ^mmr ^ Ta Clockcasks yy .'4^: -,Jf r.,-i/i,ri,r,'n Dn' Piii/tfiud as de ActJ)irei-/s />// T Jifirratini . Oct'J-fJ^o:^. ./j;Mh„U Jfii-a ^^?4J . p/. /■ A 1 > H AAr IT< G T A in , I ', /. Sl„n,:,ii 1 1. 1. ^^1_^ /'//;/' l.,:,/,/,,,///l,r,..' J;,t,/,//,,,/ „.i //,f .If/ /JiiY.fs In/ n.7hry - (ia:..r,. i-^o:^ ( 49 ) Of the Ladies' Work Tables. Plate XXVI. The table on the left is intended to afford conveniences for writing, by having a part of the top hinged in front to rife up. This rifing top when it is let down locks into the frame, and fecures the bag where the work is. The ftandards on which the table frame refts have tranfverfe pieces tenoned on, which fcrew to the under fide of the frame. The drapery which hides the work-bag is tacked to a rabbet at the under edge of the frame all round. The defign on the right is fimply a work table; the upper frame, to which the top is hinged, is about two inches broad, made feparate. The pillar is fixed to the bottom of the bag, which is a round frame made of wainfcot, with a flretcher acrofs each way, for the purpofe of fixing the pillar to it, and to firengthen the frame. The upper frame, already mentioned, is connedted with the lower one by fmall upright pieces tenoned in, after which the bag is formed of filk, and tacked to each frame, and ornamented on the outfide with drapery. Of the Drawing table. Plate XXX. This table will be found highly ufeful to fuch as draw, it being defigned from my own experience of what is neceflary N for ( 50 ) for thofe who pradtife this art. The top of this tahle is made to rife by a double horfe, that the defigner may ftand if he pleafe, or he may fit, and have the top raifed to any diredlion. As it is fometimes neceflary to copy from models or flower-pots, &c. a fmall flap is made to draw out of the toji, which may be raifed by a little horfe to fuit any direction that the top may be in, fo that the model or flower-pot may ftand level. The Aiders at each end are neceflary for the inftruments of drawing, and for a light to ftand on. The long drawer holds paper, fqiiare and board, and thofe drawers which form the knee hole are fitted up for colours. Of the Drawing Room. Plate XXXI. and XXXII. With refpe<51: to the fedlion, it is only neceflary to obferve, that the pier table under the glafs is richly ornamented in gold. The top is marble, and alfo the flielf at each end ; the back of it is compofed of three pannels of glafs, the Chinefe figure fitting on a cufliion is metal and painted. The candle branches are gilt metal, and the pannels are painted in the ftyle of the Chinefe ; the whole producing a brilliant effedt. The view, Plate XXXII. contains an otomon, or long feat, ex- tending the whole width of the room, and returning at each I end V/. pi.i J -J L_ J*itra&?n (/^-l . r".// pi i ATiTEW or THE South end of the Pifukce oFl^^AlLK3's (CiHKi'.sE BHiw^wG Room. Tl .?/ ^mm: IJlurtibn dii. J^^rAvf/,1^, J'uMt?i^,tjMrJ./.Ay^/j.Ar /^nrf,-- (IfT 0.'*/7P^ ^Awis'G Room, I'l.az. ^rSia-Zinr _/S«^. A VlE^W OF THE iPRir^CE OF IC'^ILilGS'S OiliirTKSJE iDKAWllTG ROOI xy4^. 7>f ii TMtrmAn .^lAj, JhM/?iA/ .tj l/i^ArJ dim-/j. Ay /?. 7h-ry - M>r. "^ lfi;o .1 . ( 51 ) end about five feet. The Chinefe columns are on the front of this feat, and mark out its boundaries. The upholftery work is very richly executed in figured fatin, with extremely rich borders, all worked to fuit the ftyle of the room. Within this otomon are two grand tripod candle-ftands, with heating urns at the top, that the feat may be kept in a proper temperature in cold weather. On the front of the otomon before the columns are two cenfers containing perfumes, by which an agreeable fmell may be difFufed to every part of the room, preventing that of a contrary nature, which is the confequence of lighting a num- ber of candles^ The chimney-piece is rich, adorned with a valuable time- piece, and two lights fupported by two Chinefe figures ; on each fide of the fire-place is alfo a Chinefe figure, anfwerable to thofe which fupport a table on the oppofite fide, under which is feated a Chinefe figure. Over each table, the fire-place, and in the center of the otomon, is a glafs, which by their reflecflions greatly enliven the whole. The fubje^s painted on the pannels of each wall are Chinefe views, and little fcenes. The carpet is worked in one entire piece with a border round it, and the whole in effea, though it may appear extravagant to a vulgar eye, is but fuitable to the dignity of the proprietor. N. B. In: ( 52 ) N. B. In addition to what has been faid on perfpecSlive in the firfl; work, I would here annex a few remarks on taking the geometrical or original meafurements of a piece of furniture drawn in perfpe6tive, fuppofed to be deftitute of any lines or fcales. In Plate XXX. is therefore inferted a view of a bookcafe, figure K,- which the reader muft imagine to be without any lines except thofe which form the outline of the piece. It muft, however, be premifed, that a workman be acquainted with the proportion of fome one or other of its parts, without which nothing can be done or afcertained. He muft alfo be acquainted with fo much of perfpedtive as to know that a line pafling through the diagonal of any fquare, if produced, cuts the horizontal line in the point of diftance. Thefe being known, proceed firft to find the horizontal or vanifliing line by producing c d, the top of, and /r, the bottom of the under part, till they meet in a point, as at j, which will be the point of fight ; through s draw a line parallel to the front of the bookcafe, which will be the horizontal line fought for. From the point of fight draw at random lines forward from />, and <?, or any other point that may be neceffary. Next find out the point of diftance, without which the depth of the ends cannot be known : in or- der to this, the workman muft recolledl that the brackets are always 37V'- /"■•'■ PL3(K 4-^ A Gouty HtooIj r. ^/(inihii IJ,/. ,t (,i/,lini// Dime'. /"///'/////,// f'.s ///!■ .Irt /)/nrAs /jy trTern/. •'>'/'•';. '/'/A'- ( 53 ) always as long at the~ ends as on the front, and that therefore they form a fquare block; wherefore take 4/, and place it from/ to ^, and from »■ to /j, the end bracket will be the dia- gonal of a fquare, whofe fide is 4/; produce the line ^- ^, which will cut the horizon at D ; the diftance, as the line on the leg of the gouty ftool, palTes to the diftance which is out of the plate. Laflly; from D draw lines forward through r and 10, or any other part, till they cut the front line, as at i w, by which will be difcovered the proportion that the ends bear with the front, and how much the lower part projects before the bookcafe. Now if there be a fcale of the front already to the defign, then the whole can be determined ; for by taking the compafies extended to a foot, and repeating it on the perpendicular line from a to /, the height of the doors are known, and by the fame rule the height of the pediment from / to ;;/. Then if the fame compafs be applied from / to zv, the depth of the lower part, it \yill be found vaftly out of proportion with the front, which I have done on purpofe, to ftiew that by a comparifon of this fort the errors of a defign in point of perfpedtive may be difcovered. If, however, there be no fcale to the defign, then it will be necei- fary to aflign a certain portion for a foot, as near as we ca-n judge, by confidering the common length of a bracket, from / to 4, which in general is about four and a half or four inches, which repeated three times, finds a foot, as in this cafe, and then Q it ( 54 ) it appears that the front is four feet long, and better than four feet high, that the doors are five feet nine high, and fo of the reft. But if there be no bracket, any other part may be taken whofe meafure is known, as the partition of a drawer, which is generally feven eighths thick, the height of a llider, about thirty- two inches, or the depth of a fecretary drawer, about ten inches. The ufefulnefs of this method is not confined to pieces of furniture, but may be applied to any kind of regular perfpec- tive. A Defcription of the Additional New Plates in the Second Editiofi of the Cabinet-Maker and Vpholjlerer's Drazving Book, Plate XXXI. A Sideboard. This defignis intended to have a brafs rod behind, contain- ing lights in the center and at each end. There is alfo a narrow mahogany flielf about three inches and an half wide, fixed againft the middle of the rod at the back ; on which flielf a channel is w^orked by a plane, for the purpofe of keeping up fmall diflies placed in the fpaces between the larger ones which reft on the fideboard top. The frame of this table is riclily carved out of the folid wood ,V«> pi 3 ANEW Design of a Bookcase &"svKiTEsrG Drawer />/jff ^ M^wm±ii j njJAuWI '. VM^\y *■ MM ( f ( n t [' ^SAeruifn . Jf/ JiiUz/^i^as tAt^iih/f/rcfyJy i?. Terry . lu^te 2c\ /^^4 . i^-T^i fy Scu^ ( 55 ) wood, and the ornament of that part of the legs, wliich crofs the frame, is formed m hnitation of a trufs leaf. The vafe under the table may be of mahogany, ami fitted np in the infide to hold wine bottles, or it may be confidered merely as ornamental. Plate XXXIX. A Bookcaje with 'Writing Drazver. The writing drawer reprefented out, has only the ap- pearance of a frieze when in, it being but one inch and three quarters or two inches deep. This drawer is thrown out by a fpring fixed on the back framing, and when in, is retained by a fpring thumb-catch, which ftrikes into a plate fixed on the fide of the drawer. The place where the thumb prefles is the center of the patera at each end of the drawer, as fliewn in the defign, which relieves the fpring behind, and confe- quently the drawer comes forward, fo much as to afford hold for the hands to draw it entirely out. The drawer is locked by the door lock below, which is fo contrived as to fend the bolt upwards into the under edge of it. In the lower part are clothes-prefs flielves, and the glafs doors above are intended to have looking-glafs in the center fquares. ...... 4 I.aftly, ( 56 ) Laflly, the drapery is of green filk, fixed firfl to the cur- tain, and then both are pinned on to the infide of the door- framing together. Plate XLIX. New Dejtgf is of Chair-backs* LiTTE needs to be obferved refpe6ting thefe, as the plate of itfelf fufficiently exprelTcs what they are ; if, however, any of thefe be thought too crowded with work, they may be re- duced to a ftate fufficiently plain without doing the leaft in- jury to the outline of the whole, as in the following manner: No. I is intended for painting, but may have the drapery left out under the top rail, by means of fubflituting a plain upright bar in the middle. No. 2 may be reduced by taking away the fide foliage, and making the bottom of the banifier plain. No. 3 may be either a drawing-room chair painted, or it may be made a handfome parlour chair, by taking out the top drapery and making the bottom of the banifter plain ; if for a parlour chair, the top rail is intended to be fluffed and covered with red or green leather, or it may be entirely of mahogany pannelled out of the folid ; but if a drawing-room chair, it muft be fluffed and covered to fuit the feat. No. ;za; •: r^ yi; nnii iin mrr] ^JhJC ■ki^ata TTriiMllllllllMMII ■' Ill 1 1 1 1 1,1 nmiiii 7- -y -7^-- jf 7—rr" ( 57 ) No: 4 is a painted chair, with tlie back feet at top, formed in imitation of the Ionic capital. The drapery in this alfo may be taken away without hurt done to the general outhne. No. 5 is a painted chair, and may be fubje(n: to a variety of alterations ; it may be executed with good effedl without any thing, except the three compofite columns, and two 'arches in the top rail. The remaining part of the rail on each fide of the bafket of flowers may be neatly pannelled iia the painting ; or the diamond part may be retrenched, and the two fmaller pillars with their arches retained. No. 6 cannot well be fubjea to any alteration, excepting that the ornament in the arch may be turned into a ftraight bar. No. LII. A turkey Sofa. These are genteel feats introduced in the moft fafhion- able houfes, and are an imitation of the Turkifli mode of fitting. They are therefore made very low, fcarcely exceed- ing a foot to the upper fide of the cufliion. The frame may be made of beech, and muft be webbed and Ilrained with canvas to fupport the cufliions. P The ( 58 ) The back ciifliions in this defign have fpaces between them, with drapery inferted, but they are generally made to fill clofe up without leaving any intervals. In rooms where there are no columns nor architrave fuitable for fuch a feat, thefe may eafily be put up in a temporary way, fo that if requifite, they may be taken down without any injury to the room. The back of the fofa, by which I mean the wliole height of the wall, from furbafe to cornice, mult have a deal frame fixed to it, againft Which the canvas, drapery at the top, and the fluting, muft be tacked. Plate LXVI. A Commode. The top of this commode is intended to be white ftatuary marble. The ornaments are painted on fatin wood, or other ground ; at each end is formed a niche in which may be placed antique figures. The legs of the commode ftand clear. The doors ^ each end are made to Hand about three inches clear of the feet, fo that the door will open fquare out. The internal part is merely plain flielves, as thefe pieces are never intended for ufe but for ornament. Plate LXXV. Bed Steps. The defign on the right contains a bidet behind, which runs in as a drawer. For the purpofe of raifing the bidet 4 drawer C 59 ) drawer to a proper height, the cafe is made double, one fitting within the other, as fhewn in the plate : for provided the outer cafe is made nine inches deep, the inner one, being at leaft eight, would, when raifed up, make it eighteen inches high, which is fufficient. The inner cafe is kept up by a couple of wooden fprings, one at each end, which are fo made and fixed to the infide of the outer-cafe, that the thumb may relieve them fo that the bidet will fettle down even with the edge of the cafe. The fecond ftep, which forms the night-table part draws out, and the ftep which covers it rifes tzp and falls againft the upper ftep, which forms a pot cupboard. The fteps and rifers are ufually covered with carpet, and the fides caned. The defign on the left, when the top is down, forms only two fteps. The front of the upper ftep is hinged to the top, and the top to the back ; and to keep it in its place when , down, the workman willobferve, that a groove is cut in the ends, not in a ftraight direction, but near the bottom; the groove is perpendicular to the feat ; a pin is then fixed to the under fide of the front at each end, which works in the aforefaid grooves, and the perpendicular part of the groove, which is obvious in the defign, affifts in throwing the front upright when it is down upon the feat, Plate ( 6o ) riate , A Library Bookcafe. The middle lower part of this bookcafe may have warcT- robe flielves, the reft is fimiiflied with plain Aiding flielves for books only. The circular wings of the upper part may be glazed, or finiflied without glafs, by a green filk curtain only, with its drapery at the top. The diamond part is intended to have looking-giafs inferted, which has a pretty efFedt. The pannels of the lower doors do not come flufli with their framing by a ftrong eighth of an inch, which both looks better, and is more calculated to hide the defedls, if the pan^ nel fliould Ihrink. The workman muft obferve, that the plinth, furbafe, and cornice frames, are made and finifhed entirely feparate from the carcafes, and are fcrewed to thern to keep the whole together. A DESCRIPTIVE \ A !New Design op aLadys secretary i" Cabinet Ji'^S./ii.S Fl. fJ-h T. S/uraToaJJtl. j: l'nUi>o// MmC Jid/if)u</ as t/u ActJDirrrts hi/ u Ier7-i/, 4^' ?/.'^iy*. AN ACCOMPANIMENT TO THE Cabinet-maker and Upholflerer's Drawing-Book. Injlru&ions for Drawing Ornaments. As a proficiency in the art of drawing ornaments depends chiefly on the habit of copying and the natural turn of genius in this way, a few hints only are neccflary for the aflillance of the learner. Some infl:ru6lions, however, are certainly neceflary, as ap- pears from the frequent applications that are made to matters for their information. And though no written inftrudlions can fully fupply all that may be derived from a mafter *, yet fuch direcStions may be given, in letter-prefs, as greatly to facilitate the attainment of this ufeful branch of drawing without a maf- ter's help. The principal art of every branch of drawing is included in the difpofitiun of a few fimple lines of but two different fpecies, * One very material advantage derived from a mafter is, that the pupil fees how he pradifes, by which he may acquire his manner and ftyle. A the ( 2 ) the right line and the curve. Of thefe two are compofed all that infinite variety of lliapes that wc are able to fee and con- ceive. I will, therefore, propofe to the learner, firfl: to begin with drawing, by the hand, right lines a tolerable length parallel to each other in all direflions ; firft, inclined to the right, as ap- proaching neareft to the art of writing ; fecondly, perpendicu- lar ; thirdly, inclined to the left ; and laftly, horizontal and at right angles with thofe perpendiculars, and palling through their center. A proficiency in this is certainly the firft ftep in draw- ing, and is not fo eafily attained as may be imagined. Secondly, let the learner then proceed to draw by the hand a circle, as large as poflibly he can without moving the wrift. And it will be proper for the learner to obferve, that in being able to draw a circle by the hand and eye he thereby draws curve lines in all poflible pofitions, as perpendicular, inclined to the right and left, and horizontal. In addition to this pradlice it will be necelTary to draw one circle concentric with another ; that is, as when two or more circles of different diameters are drawn from one center. This becomes ufeful when any thing is to be defcribed in the fhape of volutes, as the running foliage frequently introduced in friezes and pilafters. What has here been faid of the circle will alfo apply to the pra(5lice of drawing an 3 ellipfis ( 3 ) ellipfis by hand. An ellipfis may be confidered as a curve con- lifting of a number of fegments of circles compound, whofe radii differ in length. Of this kind of curve are many of the turns in ornament, and therefore the practice of drawing them M'ill be found worthy the attention of the learner. To pra6tife as has been defcribed I confider as indifpenfably requilite to a ready and perfedt attainment in the art of drawing ornaments ; and ought particularly to be recommended to youth, as a help to their writing any kind of hand, or drawing the Roman letters. The learner who is advanced in years w^ill not, perhaps, fubmit to this kind of teaching : but if he cannot already draw right lines, of fome length, parallel in all pofitions, and a circle tolerably near by the eye, he ought not to be above learning it, becaufe the time that is fpent in this, will be deducted in future by a more fpeedy progrefs in the art of drawing orna- ments. And however this may be thought of by fome as a thing of no merit, yet we will venture to affirm, that the hand of a real mafter may be certainly diftinguiflied by the manner of drawing thefe. A 2 Of ( 4 ) Of Copying Ornaments. Plate I. Suppose C to be the example to copy from. Take a black- lead pencil, and draw at B the principal curve-line at the bottom very faint •''. Then proceed to form a rude Iketch of the out- line, obferving carefully each projedling part of C, that a fuf- ficient breadth or fpace may be taken within the out-line, in which may be formed all the diftindt parts of B, without re- ducing their proportion. Upon this procefs corredlnefs and difpatch very much de- pend. Therefore, if upon the firft attempt of this there fliould appear any defedl, it will be befl to take out the lines with the India rubber, and make them perfect. A carver or fculptor proceeds upon tliis principle until merely the maffive parts are made out ; and it is well known that thofe of the greateft flvill in thefe profeffions are always employed in this part of carving and fculpture. After having done this, proceed to give the diftindt forms of each leaf and rofe in faint touches, that if there fliould be any caiife for alteration it may be more eafily efFe6led. The * To hanJle a pencil is, in many cafes of drawing, different from the manner of hold- ing a pen. In handling a pen, the ends of the fourth and fifth fingers reft on the paper ; but in managing a pencil, the hand is turned over more to the right, and refis on the knuckles of the little finger. learner y"p. />/■'■ <-J//<ty//ff-/M ('/ (V?/<f/t/('f//-^r^r///e ,\rr/-r/,te o^ rJii7r?f)^ro /'f /. T'.'^A/'^-.T/rft ttfiH . /^d/ffT,^ .'./ ^^ Acldi>^,-A(t /.\ 7J/yt:— July ^ zj^qS. ( 5 ) learner flioukl, in doing this, carefully obferve and touch the fibres of each leaf, and give the proper lead to each ftem, fo that they do not cut each other. Laftly, take a view of the whole, and confider in what point the light is to ftrike on the ornament ; and on that edge of the leaves and rofes oppofite to it, retouch and ftrengthen the outline in fuch a way as to give relief and effc6t to the whole, even upon fuppofition that the drawing is to remain a mere outline. Of Shading Ornaments. If the ornament is to be fhaded with Indian ink, mix fome of it thin and clear, and take a crow-quill pen, or fine camel- hair pencil, and touch the outlines very faintly, fo as fcarcely to be feen on the light edges of the ornament ; becaufe in na- ture there is, in reality, no outline on the light fides of objedts, efpecially if the fun is fuppofed to fliine on them. After this, touch the ftronger parts of each llem and fibre, that they may not be loft when the pencil marks are expunged. Having cleaned your drawing, take a large camel-hair pen- cil, and dip it till it flow freely with Indian ink very thin and clear. And obferve, that if the ink do not w^ork with freedom on a piece of wafte paper, which fliould be kept for the pur- pofe ( 6 ) pofe of trying the pencils, the brufli in this ftate ought not to be appUed, but iliould again be well worked in the thin Indian ink, fo that it work cafy, without, leaving white fpots on the paper. In this ftate apply the pencil to the ornament, and give a general tint to thofe parts fuppofed to be all in fliadow ; at the fame time a partial tint may be given to the objeas partly in the light. This flrft courfe of Ihadowing is the great balls of all real efFe6t ; for if the maffes of light and fliadow are not pro- perly parted, but confounded, the drawing will look heavy, un- intelligible, and boyifli. When the drawing is properly diy, the laft tints are to be given with great delicacy and care, left the whole be over done, and, as it were, tormented with harlli dabs. The intention of this laft tint is only to give refleded lights to thofe parts which he in the mafs of fliadow, and fliarpnefs to the partial fliadows diredtly oppofed to the light. It is natural for the learner, in giving the laft tint, to think of thickening his ink ; but this muft be avoided, as dangerous to the cffe6t of ornament ; for if the ink at firft ufed be again repeated on the former tint, it will give fuffici- ent colour, except the openings of the fibres, which may be touched with ftronger ink. Effea ( 7 ) EfFeft to ornament may alfo be given by a pen, in imita- tion of etching ; which, if well executed, is moie plcafing in ornament than Indian ink. Italian chalk is fometimes iifed along with a black-lead pencil, which may be done with extremely good efFedt. The learner, being furniflied with thcfc inftru6lions, may proceed in the fame way with the reft of the fpecimens in foli- age, the principal variety of which is here exhibited. K, is the thiftle leaf, fliarply pointed and irregulai*. G, is the Roman leaf, round and mafTy. F, the parfley leaf, light and rather fharp pointed, E, the rofe leaf, formed into groups. D, the oak leaf, broad and mafly, fcolloped on the edge, with fmall partings. A, is a fancy leaf, rather Iharp, with large partings, C, rofes and leaves alternately. With C 8 ) With thefe fpecimens the learner ought to be well acquaint- ed, before he proceed to draw running ornaments, that he may give fufficient variety in each turn. The regular leaves, in Plate XI, fliould alfo be copied, as they are much in ufe in carving and japanning. Next proceed with the borders in Plate III, which are in- tended for japanning or inlaying; and fo on with any other of the Plates, as Plate V, VII, and IV, as they may appear moft fuit- able to his abilities in drawing ; obferving in all cafes to make a very light pencil-fketch of the whole defign, before any thing is attempted to be finifhed. Of Clarifications necejjary for Conipofition. To qualify the learner for compofition, he ought, in fome meafure, to be acquainted with the proportions of human figures, efpecially thofe taken from the antiques. My very li- mited plan in publi filing thefe ornaments affords me no oppor- tunity of doing any thing in this way by example. I will, how- ever, give a few hints refpe6ting their proportions, for the af- fiftance of thofe who have no opportunity of confulting the belt matters. The ( 9 ) The proportion of the male figure, according to Mr. Brif- bane's Anatomy, from Albiniis, will be near enough, as follows: If the perpendicular height of the intended figure be divided into ten equal parts, and one of thefe parts into four, the proportions will run thus with refpedl to length : the head, from the crown to the chin, one tenth and one fourth ; the neck rather more than one third of the head ; from the fummit of the fiioulders to the bottom of the belly, three tenths ; from the bottom of the belly to the center of the knee-joints, two tenths and one half ; and the fame from the center of the knee-joints to the bottom of the feet. Gbferve, the height of the hips are fix tenths and one third from the ground, and the length of the arm four tenths and rather more than one half. In thicknefs as follows. — Over the fliouklers, two tenths and one fourth ; over the hips, one tenth and rather more than three fourths ; over the thick part of the thigh, one tenth ; the fmall part, near two thirds. Thefe principal parts being at- tended to, the reft will follow of courfe, by prailifing a little upon the different parts of the body from examples. When the proportion of any male figure is to be proved, take the thick- nefs of the thigh as one tenth of its height, and by remember- ing the above proportions any figure may be examined. By thefe proportions I have examined a figure engraved from the famous Raphael, an Italian painter, and found them to agree B exadllv. ( 10 ) exadly. In refpe£l to the female figure there is fome difference in the proportions; the whole is more flender and elegant; the flioulders are not fo broad ; the trunk or body is fliorter ; the hips broader, and in proportion higher from the ground ; and the mufcular parts are not fo flrong and prominent. As female figures are frequently interfperfed in the compofing of orna- ments, it is proper to obferve, that much depends on the ma- nagement of the drapery with which they are clothed. It ought to hang with freedom and eafe, and in fome parts to lie clofe, fo as to difcover fome of the principal fhapes. To effect this, it is beft, firft, to draw the figure by the pencil as if entirely def- titute of drapery, and afterwards to lay the drapery gently over with Indian ink, or colour, as may be required ; fo that the lines which marked out the parts of the body, now covered, may be expunged. This method gives true eflfed^ to the dra- pery, by enabling us to determine where there ought to be ftrong, where flight, and where no folds at all. On the pro- minent parts of the body there are no folds in the drapery ; but after having juft palTcd over thefe, the folds commence in ten- der marks, and increafe into ftrong folds where the drapery is detached from the body. In examining Cipriani's figures, I find, that if the afllgned heiglit of the female figure be divided into ten equal parts, from the ground to the waift. \\ here the drapery is fometimes tied 5 round, ( II ) round, is feven tenths; from the waifl to the top of the fliouldeis, one tenth and an half; the neck a quarter, the head one tenth and a quarter, and over the fhoulders rather more than two tenths. As boys or cupids are frequently introduced in ornaments, it is proper that the learner fliould take notice of their propor- tions and general appearance, as different from thofe already defcribed. Cipriani's boys are of the following proportions: — If the afligned height be, as before, divided into ten equal parts, the head will be full two tenths in height ; the neck very fhort ; from the top of the flioulders to the bottom of the belly, four tenths ; from the bottom of the belly to the knee-joint, full two tenths ; and from the knee to the ground, bare two tenths ; the arms, when hanging perpendicular, come not quite to the middle of the thigh ; the breadth of the fhoulders not quite three tenths ; and, laftly, the thick part of the thigh, one tenth and an half, v^hich will of courfe give the proportion of the leg. The learner ftiould obferve the general caft of thefe figures; the head is large and round ; the neck fcarcely diftinguifliable between the head and flioulders ; no joints appearing in the arms or legs fcarcely; the ankle covered with fiefli, and the whole leg thick and mafTy. But, belide the human figures, there are others of an ima- B 2, ginary ( i^ y ginary kind employed by the antiques in their decorations, Thefe are ftill, and ever will be retained in ornaments lefs or more. The moft tafly of thefe were feleded by Raphael, and painted by his pupils on the walls and ceilings of the Vatican Library at Rome, and which are handed down to us, by the Italians, in mafterly engravings ; which, in the courfe of this work, I have confulted, and from which I have extracted fome of my ideas, as well as from fome French works. In the Vatican are figures whofe upper part is female, andi the lower of foliage entwifting round. Other female figures have their lower part of a fifh, and fome of a greyhound. Others fliew only a human head, with foliage fpringing from it in different forms, aiifwering for wings, and for a covering of the lower parts. In it, we fee fometimes a dolphin fifh with an orna- mented tail ; a lion's head and an eagle's leg and talons brought into a fmooth outline by the help of foliage : at other times a tiger's head and paw formed in the fame manner. Some, again, are partly a horfe with wings and two fore legs, and partly the tail of a fifh ; all which are now a namelefs generation, but oace the offspring, I prefume, of the ancient metamorphofes, either what they termed real or apparent. Befides thefe, are to be feen, in the above work, the fphinx, a figiure of much fame amongfl the ancients, whofe upper part 8 is ( 13 :) is a woman's head and breads, and the wings of a bird ; the lower part the body of a dog, and the claws of a lion. This monfter is faid to be the production of two deities, and fent as a fcourge to the Thebans. Its bufinefs, on a mountain at Thebes, was to propofe dark queflions to palTengers, and if not anfwered to devour them. It is faid that the Egyptians nfed the fphinx as a fymbol of religion, on account of the myfteries which it was capable of interpreting. The Romans therefore placed it on the porches of their temples. The centaur, partly a man, and partly a horfe, ufed as one of the figns of the zodiac, in which the man part is reprefented fhooting with a bow. This being is alfo faid to be the offspring of a deity in con- jundlion with a cloud. They inhabited Theflaly ; and, engaging in hoftihties with the bow, were vanquiflied by Thefeus. As they feem to have been a rebellious race, they may be intro- duced into fuch fubjedts as are intended to Ihew the odium of fuch condu<5t. The griffon is another fabulous being, exifling only in the vain imaginations of the ancient heathen poets, as do the two former. They reprefent it partly an eagle, and partly a lion ; that is, the lower part of it. They fuppofe it to watch over golden ( 14 ) golden mines and hid treafures. It was confecrated to the fun, whofe chariot was drawn by a number of them. And thefe, if you pleafe, may be introduced into fubjedls intended to reprefent covetoufnefs ; or they may be placed over cabinets where trea- fure is kept. It will be proper that the learner fliould ftudy to compofe thefe, if he intends being a proficient in ornaments. In fhort, to be fully qualified for ornamental decorations, is to be ac- quainted with every branch of drawing. And, further, to compofe to much purpofe, it requires to have a general infight into works of this nature, and particular- ly to fee the painted walls in noblemen's houfes, in many of which the art is exhibited to its utmoft perfe6tion ; and in none more fo than in the printed and painted filks executed of late by Mr. Eckhardt, at his manufactory at Chelfea, adapted for the purpofe of ornamenting pannels, and the walls of the moft ele- gant and noble houfes. Of Compofition. After the ideas of the pupil are extenfively furnifhed in the manner now defcribed, it will be proper to begin with fome fmall ground to compofe on, fuch as the frieze of a cornice; and ( 15 ) and to confider its fituation with the eye, whether it be intended to be much above it, fo that the parts of the ornaments may fuit the fuppofed diftance of the eye from it. It is of no effect to put a number of fmall ornaments in, to be viewed at a great diftance. In this cafe the parts fliould be limple, entire, and rather mafly, to produce a proper effect. If the frieze be near the eye, it may then be divided into fmaller parts ; but to crowd it in any cafe ought ftudioufly to be avoided. And obferve, the tablets of friezes ought to be diverfe to the other ornaments in it. I would then recommend to compofe on the ground-work of a pilafter not very broad ; for it is to be obferved, that the difficulty increafes in proportion to the width, more than in the height of a ground- work. The ornaments in a pilafter or pan- nel is conlidered as growing upwards, and therefore it ought to take its rife from fomething principal at the bafe, and grow rather lighter towards the top, as in every inftance is fhewn in nature. But this does not confine the compofer to fuppofe that every thing is to be faftened or tied to each other as in ftri6l nature, for this would fometimes be the fource of heavinefs in ornaments ; nor do I fee it pradifed in the Vatican, or by any of the heft artifts in this way. But certain it is, that the beft compofitions are thofe which keep the parts moft connected in one entire piece. The more we attain to this, whilft we avoid a heavy C i6 ) heavy repetition of the fame parts, the nearer do we arrive at perfedtion ia this art. The ornaments of a pilafter ought to fill regularly on each fide, and not to leave niuch naked ground. And efpecially we ought to obferve, not to have the ground alternately crowded and naked. If we begin in an open ftyle, leaving much naked ground, this fliould be continued uniformly all the way up, and, if any thing, only to grow more open at the fummit. The laws of harmony in every art, where time, motion, and fpace are obferved, require this. If the furface to be ornamented be horizontal, and is liable to be viewed alike in all points, as in a ceiling, the fubjedt fliould be regular, and formed into pannels and groups, fur- rounded with foliage of the fame kind and form on all fides. Nature exemplifies a regularity in molt flowers, and in other things that grow horizontal. Laftly, to compofe ornaments for a large upright pannel, as in rooms, is by far the moll: difficult talk in this art. Here it is required that the artill colled; and arrange all his ideas ; and thofe fcattered fragments which exilt in his mind through long and repeated obfervation on the works of the bell mailers, mull now be collecSled to form an entire whole, by a general concourfe or ( 17 ) or aflemblage of every branch of drawing. In this large field, architedure, perfpe6tive, figures, landfcape, foliage, and fruit, may vie with each other, and fliew the mafter's fkill. Attempts of this nature may be made by the learner, and with fuccefs, though he fall vaftly fliort of a perfed; difplay of all thefe different branches of drawing ; for it is to be obferved, that the rule for judging in works of this nature is not to look for eminence in each and every difi:in6l branch, but to difcern fine tafte and jullnefs of compofition in the whole. In compofitions of this nature fomething fpreading and maffy ought to be at the bottom of the pannel, except the orna- ment be only intended to occupy the center, in which cafe the principal part of the ornament fhould be in the middle ; but where the entire pannel is to be filled up, we fhould begin as above, that there may be an opportunity of giving breadth to the foliage, for the purpofe of filling up the ground regularly from one beginning only, for two defigns muft not be entwined with each other in the manner of cyphers. This deftroys the beauty of fimplicity, which confifts in fewnefs of parts, and en- tirenefs of forms, without which all is a jumble. This obfervation will teach us to avoid that kind of crolling and cutting each other, fomething like the rigging of a fliip, C which ( i8 ) which may be obferved in fome ornaments, even of French production as well as Englifli. A practice this, which always denotes bad compofition, and a barrennefs of thought. It is done with a defign to enrich, but it only turns out to be a fill- ing up to the prejudice of the whole. The learner muft there- fore fludy to enrich by a variety of thought fpringing from fomething, yet without interfering with each other. He fliould alfo be careful in avoiding the appearance of Ilraight lines continued from bottom to top, which is formal and bad. Some continuance of a right Une is beautiful ; but it ought quickly to be broken in thefe compofitions, whether per- pendicular or horizontal. Obferve breadth in the parts, fliun niggling and meannefs, and flick at nothing that will have a comely and pleafant ap- pearance. Jn Explanation of the Plates, Plate II. are chair legs. That on the left is intended for japanning, and is formed fquare. The other two on the right are turned, carved, and gilt. Obferve, the plinth of the center foot is left fquare, and pannelled out. ^. Borders for Pier Tabi^es JVV^. pf / r/.y r.s ',■'■<,;.-, ztel. / CaUudll JJrrxrf Piiblt/hn/ as the Ad Dirtcts by G-Terri/. yov.'.s T!g;>^ ? CI Girandoles OHXAMIONT h'lil I'AIVTKD TA^M. /'/ 4 r x>^.,/,.„ />,/ fuli/i/luJ ,u r/„ AitOu-rrh (i, S Tot,, Vovn ,,„. CHAIK liEGS ^'^^ 'Um^^^ m'm unmm "^^m «if /■iiAAt'i ■/ aj Mf .Ur J/ir/fli V ti Tfrr^ — .In-/' ^ ^^ ( 19 ) If the leg on the right be thought to have too much work, the hufks in the flutes and the drapery on the phnth may be omitted. Plate III. Borders for japanning or inlaying. Plate IV. Ornament for a pannel. The whole fprings from a fpreading leaf at the bottom, from which a ferpent attempts to come at the doves on the fruit. In the center is a temple not dedicated to the interefts of the cupids, for which reafon they are burning it with their torches. The figure on the top of the column, in refentment, means to pelt them with ftones ; and the geniufes above are pouring down water to quench the flames. The owls are emblematic of the night, at which feafon thefe mifchiefs are generally carried on. The other defigns in. this plate require no remark. Plate V. Ornament for a tablet, intended for painting on a grey or blue ground, as bell calculated to throw forward the figure and fruit. In the cornices, the acorns in one, and hufk in the other, are turned with a pin ; by which they are fixed into the large proje(5ting fquare. C 2 I would ( 20 ) I would advife to work the upper part of the cornice fepa- rate, by which means the acorns will be more eafily fixed. The frieze may be carved, painted, or inlaid. Plate VI. Defigns for bed-pillars. No. I and 2 are to be painted ; No. 3 carved in mahogany ; and No. 4 and 5 are intended for rich ftate-beds, carved in white and gold. The fcale of feet and inches at the bottom will give the heights, and other proportions. The pateras which cover the fcrew heads are on loofe pan- nels let into the pillars, and which fettle down into a groove at the bottom, by which means they are kept in their place, and eafily taken out. Plate VII. Ornaments for the center of a pembroke and pier table needs no explanation. Plate VIII. Of chair fplads. No. I, 2, 3, and 6, are intended for parlour chairs, carved in mahogany. No. 3 and 4 are for painted chairs. Obferve, the curve lines which come from the top rail at No. 2 and 6 are intended to .V.K /./ IU:i) IVlMiAKS .- \Ar'..' ^ />,/ /•„/./ifAt.i f/.i tA, .Ui fhrttt-i. All (' T^rr\ . XW.'^ tt /-^.i i:"-/<'/. />i.i. Tt 7 Center for n l*EMBEOKFi Tam.e C/KNTKIR for a FlER TaB.LE r.S/lrriilrtI /If/. FtlW/ir./o^ ///, ./a/A, A /;/ /;. Tr////.— /■'f.' 2:i. /^i/t .Vjt'- pi i SPLABS TOK BMNTEI) A^^D MAHO<ykNY CHAffiS r/ N r.-i^^n D,/. PufiftfAfi/ US f/u .iff Jhrf,'ts hif li rrrrif. — /Jrr/f.'i /r^-*. J.i\.lA,^// fMff' , I. ".//-. /y/./. Lkos ^V Pn-.R an<^ Card Tables r/ (J itri r/fl^^ II 'II I i^.;^c> X° 1. NO 2. :nto ,3_ NO 4!. N<? c5. "T r n N"6. -/' ."^/ifra/cn JJt/. Pti/j/^/i€/i as //i€ Act.Urr^r/ii ^^ 6^. Terry, ^tmH ff.f-^-^. Jl f'ou/naJ^ Mttixa^ MU/. /I' 2 HTI'MI'S .V* Kl.BOVV^S ^>r DHA-WCSIG RooM C'jums /y, //' J r .^f,t'.,t.->, jj,r luM/A/,/ ii.s //ir .1rtJ)irri/s /'// /-'y^rry. Jiiii' '-f. )^^-f. /i;i/Jni' A^' ( 21 ) to fhew where the outfide fplads in a complete back will come in, anfwerable to No. 4. Plate IX. Of toes and knees for pier and card tables. No. I, 3, 5, are meant for pier tables, the ornaments of which are intended to be carved and gilt. No. 2, 4, 6, are for card tables, with ftringing and pannels let in. Plate X. Of chair elbows, with part of the feat, together with fplads for chair backs. The fplads are all intended for japanning, except No. 4, which may be worked in mahogany. The elbows are meant chiefly to be carved and gilt ; but the mere outlines of any of them will ferve as patterns either for painted or mahogany chairs, by leaving out the ornaments for the mahogany, and retaining fome of them, or even all of them may be adapted for painting. It may be proper to obferve, that as high as the fluffing of the feat a rabbet fhould be left on the flump to fluff againfl ; which is eafily done, as the flump is made fmaller above the rail. The cufhions on the arms are formed by cutting a rabbet in ( 22 ) in the arm, or leaving the wood a little above the furface. Some, however, bring the rabbet fquare down at each end, covering the wood entirely,, except a fillet, which is left at the bottom and continues round the ciifliion. Plate XI. Ornament for a tablet intended for a painting, but which might be enlarged very well. The fubjedt is a faint moonlight fcene, reprefenting Diana in a vifit to Endymion ; who, as the ftory goes, having offended Juno, was condemned by Jupiter to a thirty years fleep. It may not be improper to advertife fome, that thefe, with a thou- fand other of the fame kind of ftories, are merely the fabrica- tions of ancient poets and idolaters, forming to themfelves in- numerable gods, according to their vain imaginations, and which now, only ferve to try the painter's fkill in decorating our walls. And in oppofition to thefe vanities, I cannot well omit whifpering into the ear of the reader, that " To us there is but one God, the Father, of whom are all things.'' I Cor. viii. 6. Plate XII. Cornices for windows. The one acrofs the plate is intended for japanning, the upper one for carvmg and gilding, and the two under ones may be either carved or japanned. The I'l. /2. J. I'll/i/livt// Dil/.r,-t NUof'l.' AS"! N D 1\^ ( ' ( ) H N 1 C V. f5 /'/. f2. r .ili,r.tl,;, />,/ /^/i/>////tfi/ ii-^ t/if .iff /iirrrfa /»// it Terrt/ . />^ r W z''^* /./V-A^// />,ru.' ( 23 ) The circular ends of this cornice are fometimes formed of a faintifh curve, and fometimes of a quick one. When they are of a faint fweep, they ought to be made fomewhat longer at each end than the outfide of the architraves, to give place to the curtain rods, fo that they may be brought fufficiently for- ward on the lath, and not leave too great a vacancy between the rod and cornice leaves, otherwife the lath will be feen when there is no drapery. In making thefe cornices, it is beft to plough and tongue in the leaves to the under fide of the facia of the cornice. The ends may be formed by gluing blocks of deal one on another till they come nearly to the fweep ; and, after having formed the outfide curve, I would then advife to gage on for the plough-groove for the leaves, before the wood in the infide is brought to its form, that the pieces for the leaves may be put in without fplitting off the groove. After thefe are well dried, then the fuperfluous wood on the infide can be taken away. When the cornices are made at each end with a quick curve, the whole is firfl worked in flraight mouldings, and mitered together at each end, the fame as if intended to be fquare, according to the old fafhion. When they are glued in the miters, get out blocks of deal, about two inches and an half fquare, and cut them down anglewife, and let their length be equal to the width of the cornice and length of the leaves. 7 After ( 24 ) After thefe blockings are dry, cut off as much of the old miter as isfufficient to form the curve, and work the mould- ings again by hand ; and obferve, that as the block was left long enough, the curved leaf is intended to reft againft it, by which it will be much ftrengthened. The cornices made thus, with a quick curve, needs not be made longer than ufual, becaufe the quick curve admits the rod to come forward more eafily than the other. Plate XIII. Pilaflers for Commodes. Thefe may be painted, inlaid, or gilt in gold behind glafs, and the glafs being then beaded in the pilafter, it is fecure, and has a good efFedt. Plate XIV. Chair Legs. The center leg is worked fquare ; that on the right is 0(5ta- gon, except the vafe at the knee ; and that on the left, round. Thefe may, in the view of fome, be thought too full of work ; but the fkilful workman will eafily fee how to reduce their richnefs, and accommodate them to his purpofe. FINIS. PlLASTEBS FOR (' 0M3IODE S r/ fii fiMl/f/l',/ ,IJ Ht All /Mr,./., /,!/ o Teiru- — M' ll.ryift J.U^WHim. !>i !iv > I— I si 35 C/5 ("HAIR LKOS "^fM^M/HtU^tUt* Mm ^M !l 1^ » ■ ' ■: mm fi/A/i-.^,./ .,. '/, /^r />//-/,ii iJj, ii.Tfrry~—Mj/.' /^'' DESCRIPTIVE INDEX. PLATES. XXII. Ditto, for fmaller library, inclofed in a Pembroke table - to face page 44 LXXV. In additional dejigns. — Ditto, one with night-table only, the other with night-table, a bidet, and put up board - _ ^g TABLES OF VARIOUS KINDS. XXV. Table univerfal, to anfwer the purpofe of a dining and breakfaft table, with a drawer divided into boxes, for tea, fugar, &c. When ufed for breakfaft table, its flaps Aide under the bed _ - _ XXX. Ditto, for Library, with four niches or knee holes, four cupboards and four drawers, tvvo of which with rifing reading defks XXXVII. Ditto, for a lady to write at, with fcreen to rife up by weiglits behind to fave the fice, and fpring writing boxes, after the French - - . XLIII. Ditto, on a fimpler and more eafy plan, with fcreen behind fupported by fprings -----__ XLTV. Ditto, one to read, and the other to write at - - - XLVI. Ditto, for a lady to drefs at, with a glafs in the centre, and one on each fide, as refledters, framed fo as to move to any pofition; under the dreffing part is a knee hole forming a cupboard, and at each end a drefs- ing drawer to hold caps - . _ LIV Ditto, for a lady to work at, has a rim round tlie top, with one fide of it hinged, fo as to turn down to a horizontal pofition _ . _ Ditto, for breakfaft, containing a bidet and two glaffes, fupported by pillar with four claws - - - - - LVI. Ditto, a Harlequin Pembroke one, witli a neft of drawers to rife out of the top, with a falling flap to write on - - - LVIII. Ditto, of the fhape of a kidney, for writing and reading, by a rifing defk which Aides forward ; at each end are a number of finall drawers LX. Ditto, to draw and write at, has a rifing flap, lined with leather, a neft of drawers in the upper part, letter box and cupboards, the top edged about with a brafs rim, the lower part confifting of plain drawers V. Aipendix — Table for piers, or to ftand under a glafs, finiftied in white and gold - - -.---_... VII. Ditto, for dreflTing, with glafs to rife behind, convenience for wafhing, and a bidet ----__. Ibid. Ditto, to ufe in the night, conneded with a bafon or wafti-hand ftand, and pat cupboard, with reeded door . - _ _ _ XI. Ditto, for cards; one fafti plain corners, the otlier with column corners and •round front -----__ XII. Ditto for Library, of an elliptic iliape ; contains a fecretary drawer to write at ia a fitting pofture, and a rifing delk in the top, to ufe in a ftanding pohtion ; the back part is fitted up for books, and each end has four or five heights of plain drawers. - . _ XX. Ditto, a plain one for dreffing, with glafs in the centre, and a writing Aider at the end - - - _ _ JCXIII. Ditto, for night ufes, to ftand in a corner ; one connedted with a bafon- R Hand, 362 376 390 396 398 414 ib. 430 432 440 8 12 ib. ib. PLATES. XXVI. XXX. DESCRIPTIVE INDEX. fiand, turning round on a pin, by which the night-table part is totally hid, the other with lifting top, &c. - - to face page \h Ditto, for a lady to work at ; one with a drawer to write a note on fup- ported with two lyre ftands; the other with a pillar on four claws, and only a work bag - - - - 5° Ditto for drawing, with a double rifing top, capable of being elevated to any height, has a Aider at each end to lay drawing implements on, and one under the top, on which to place a model, &c. to copy from - ib. vm. XXX. XXXIX. LI. LVI. WARDROBES. Wardrobe with two wings, containing arms to hang clothes on, tlie upper part has clothcs-prefs (helves, and the lower plain drawers - - - Gouty Stool, made with a double horfe to raife the leg to any height Knife Cafes, ornamented with pilaflers, and pillars in front ; one with ogee and hollow front, the other with two hollows, and a round in centre. - - - - " . T . " Window-curtains and drapery in the French taftc, exhibited with glafs and pier table, flievving the effedl of the internal front of a fmall draw- ing room __----- Ornament for a tablet, conhfting [of parfley foliage, fpringing from the tail of a griffin. . _ - - - SO 392 406 43 A DESCRlPTtVB A DESCRIPTIVE INDEX TO THE ACCOMPANIMENT TO THE CABINET-MAKER AND UPHOLSTERER'S DRAWING-BOOK, CONSISTING OF VARIOUS ORNAMENTS. PLATES. I. Specimens of various foliage, for the exerclfe of learners, including the thorn, parfley, oak, and rofe leaves, together with others of fancy ..---- to face page 9 11, Chair legs, near the full fize, richly ornamented for white and gold, but may be reduced to a plalnnefs fultable to mahogany chairs - - 20 III. Borders for pier tables, which may be executed in japanning, or in- laying - - - - " - ID. IV. Two patterns for girandole lights fupported by figures, richly orna- mented ; a trufs cornice and frieze for a pllafter, and a fpeclmen of a richly ornamented painted pannel, confifting of a temple fet on fire by Cupids, whofe intentions are defeated by the interpofitlon of certain genii, who pour down water to quench the flames - - - - ib. V. Ornament for a tablet, and two fpecimens of new fancy cornices, with handfome friezes ; the tablet is a boy fupportlng a bafket full of rich flowers and fruits _ - - - 21 VI. New and elegant bed-pillars, two of which for ftate beds, to be executed in white and gold; one for mahogany carved, and two for japanning - 22 VII. Centres for pier or Pembroke tables, either for japanning or inlaying ; in the centre of the Pembroke tables, the genius of poetry, painting, and mufic, are aflfembled - - - - ib. VIII. Six various patterns for fplad-back chairs ; four may be executed in ma- hogany, and the remaining two for japanning - - ' - ib. 8 IX. Six DESCRIPTIVE INDEX. PLATES. IX. Six various patterns for table-legs : two for rich pier tables in white and gold, two for plainer tables, and two for card tables - - to face page 22 X. Six different patterns for ftumps and elbows of drawing-room chairs, fliew- ing part of the rail and feat, and in two the intire leg ; alfo five various fpecimens of chair fplads for painting - - - 1% XI. Ornament for tablet, exhibiting Diana and Endymion, in a faint moon- light piece, ornamented with foliage ; alfo fix various fpecimens of leaves for carving - -- - - --24 XII. Four various patterns for window cornices ; one for a grand faloon room, to be executed in white and gold ; the others for japanning - - 25 XIII. Three various fpecimens of pilafters, for commodes or cabinets, which may be executed in inlaying, gilt on glafs, or japanned - - - 26 XIV. Three patterns of chair legs near the full lize, to be executed in white and gold ._-_--. -.-2^ DESCRIPTIVE INDEX TO THE SEVERAL PIECES OF CABINET FURNITURE CONTAINED IN THE WORK; INCLUDING THE NEW AND ORIGINAL DESIGNS, ADDED IN THE SECOND EDITION, ALPHABETICALLY ARRANGED. BEDS. PLATES. XXXl. XL. XLI. XLV. I. III. IX. XIX. A Sofa ditto, with dome top and French drapery ; on the fide of which is a view of its perfpe(9:ive lines - - to face page 380 Alcove ditto, reprefented on afcending fleps, covered with carpet and dra- pery round the arch of the alcove _ _ _ 382 A Summer ditto, made in two feparate parts, with a dome to each part, an ornamental arch at the foot, and both connedted by one head ; intended for a gentlemen and lady tofleep apart in fultry, hot weather - 384. A French State ditto, with dome top, ornamrtited, and with double head, exhibiting the perfpedtive lines according to its oblique fituation - 386 ylppendlx — Elliptic Bed, dome top, with drapery, ornamented cornice, me- dallion-valence, and couch ends . _ - - 6 A Duchefs ditto, in three parts, ftraight cornice, cove top to take off, and drapery covering _.._-__ 6 A common ditto, with drapery valence, and cove top, ornamented - 16 Englifli State ditto, with dome top, and crown fupported by Juftice, Cle- mency, and Mercy; the cornice, pillars, &c. adorned with various fym- bolical figures, expreflive of the different branches of the Britifh govern- ment - - -._ --40 BOOKCASES AND DOORS. XXVII. Six various Patterns of ditto 370 XXIX. Six DESCRIPTIVE INDEX. PLATES, XXIX. XXV II. XXVIII. XLVIl. LVII. XXXIX. III. XLII. to face page 370 5° Six ditto ditto . - . . . appendix. — Eiglit ditto ditto . _ . Bookcafe, with fecrct.nry drawer, glafs doors, pediment top, and clothes prcfs Hiclvcs ill lower part - - - - -370 Ditto, with cylinder (1e(k, Aider fixed to cylinder, plain, fquare-figureddoor, with green filk curtain, and drapery at top - . . Pediments for ditto, ornamented and plain - - - 4J2 Li addiiioriiil lu-v.- pintcs. — Ditto, with writing drawer, clothes-prefs ftielves, and ornamented pediment, ligured door, and green lilk curtains, with drapery -- - - ~ ~ ~ Si Library ditto, with circular and ftraight wings, glafs doors, with curious figure; the circular- winged doors notgl,v/.cd, but finiflied in fluted filk, with drapery at top ; the lower mid<ile part contains four clothes-prefs flu'lvcs . - _ - . _ _ 8 Library ditto, with circular wings, dome top on each, and ornamented pediment, gLfs doors, with green curtains, and drapery at top Bafon Stands, to ftand in a corner; one with a ciftcrn, and another with tops to fold over ______ 294 CHAIRS. XXXII. Chairs for drawing room, fluffed back and feats, finiflied in white and gold - - ----- 388 XXXIII. Ditto for parlour, finiflied in m.diogany - - - - ib. XXXIV. Ditto for drawing and parlour - - - - - ib. XXXVI. Ditto, fix new Patterns for Backs ; fomefor ia(>aiiniiig, atxiditto for mahogany ib, ,, VI. Appendix — Ditto for drawing rooms, finiflied ; one tor japanning, the other for white and gold - - - - - -12 X. Ditto, Convcrfation, made with ftufFed toprails, to reft the arm upon ; the fc.its made narrow in fiont, but longer than in common from back to front -'- - - - - ■■ 16 XXV. Ditto, fix new Pattams of Backs for painting - - - 48 XXV III. Ditto, fix new ditto ditto - - - "5° XLIX. In the additional dc/igns of the fecond edition. — Ditto, fix new ditto ditto.— See their dcfcriptioK at the end of the appendix - - 56 XVIII, Afpcm/ix. — Chaife Longs, or Long Chairs, ftutVetl and covered in the man- ner of fofas - _ . - . -26, CABINETS, XLVIII. Cabinet, with the pcrfpeftive lines. The upper middle part for books, and the wings for medals, rings, &c. and other fmall curious matters ; the lower part is divided into drawers and final! cupboards XLIX Ditto, with drcfiing table. Lower part contains convenience for a lady 8 406 to PLATES. L. XIV. XVI. DESCRIPTIVE INDEX. to warti and diefs at ; the upper part a fvving glafs in center, and each wing is comparted for trinkets, &c. - - to face page /\.o(> Ditto, with convenience for writing, for holding books in top part, and a private cupboard at each end, with dome tops - - 408 Ditto, with branch hghts, and convenience for writing in the top part; together with finall drawers, and private places - - 22 Ditto, with a felf-balancing front, and convenience at each end for tea equipage . - - _ . .33 T' COMMODES. XX. Ditto, for dreffing; containing neceffary apparatus for walking, witli a glafs in the center, various boxes for powder, 6ic. and a convenience for wri- ting a note - - - - - ^, LXVI. Ditto, for an ornament to ftand under a pier glafs ; has a figure at each in a niche, and a white flatuary marble top ... LIX. Cornices at large, in various prcrtles; together with furbafe mouldings, and the method of enlarging and contrafling them pointed out XXIX. ^/)^«d'/W. —Clockcalcs, to be executed in latin wood if the ornaments are introduced on the doors ; if not, they may be executed in mahogany, with good effedl --___. LXI. Drawing Room, plan and fe(flion of, complete ; and a view of every necef- fary article of furniture in their proper Hruation XXXII. Appendix. Ditto, the Prince of Wales's, with Chinefe furniture, in a feftion, and perfpedlive view - - - - LX. Dining Parlour, with proper furniture'to do, exhibited in a perfpedlive view 40 58 43 50 445 52 440 SECRETARIES. XXVIII. Ditto and Bookcafe, with clothes -prcfs fljelves, 'figured docH-s, and pe- diment top - - . . - _ 5g5 XLIII. Ditto, a Lady's, with book-(helves at top, fupported with brafs pillars; has a cupboard at bottom for hats - - - ib LH. Ditto, a Gentleman's, with felf-balancing front, and two wings for books, with glafs figured door, and ornamented lop _ _ - 410 XXXIX. In additional new plates. — Ditto, a fnjall one for a Lady, with falling front, and writing drawer - - - ~ - SS SIDEBOARDS. XXVI. Ditto, with celleret drawer for wine, a plain drawer, and pot cupboard at the other end ; (Iraight front, and fafli-plain ends - - 366 XXIX. Ditto, with celleret drawers, hollow front, and round ends: one end opens with PLATES. XXI. XXXI DESCRIPTIVE INDEX. with marble fhelves, for fmall filver ware ; and the other enclofed^ for a pot cupboard - - _ - _ to face page 370 Appendix. — Ditto, with vafe, knife-cafes, and pedeftals at each end, with ornamental brafs rod and lights; ^a celleret drawer, and plain ditto ; and a pat cupboard in center, hid by a reeded front, forming a recefs to tlie arch under the front arch - - - - - \z In additional new plaUs. — Ditto, witii carved front rail, and trufs ornaments on the legs, and an ornamental vafe celleret placed under the fideboard 54 SCREENS. XXXVIII. Ditto, tripods, for japanning - _ _ _ ^90 XIII. Appendix. — A Tripod one, and Horfe ditto. The tripod one, for white o and gold, turnson a fwivel, fo that both fides of the mount are finilhed alike ; ditto, the horfe balance is of mahogany, with its uprights fluted or reeded - - - - - - 20 STANDS OF VARIOUS KINDS. XLTI. Stands with corner wa(h-hand ones in three different patterns; one ditto with water ciftern and lock, inclofed with reeds, and a cupboard below to throw off the dirty water; one ditto plain and common; one ditto with folding tops when up. to prevent tlie wall from water fplafhes - 3^4 XLIII. Ditto, made fquare, with ciflern at top, plain drawer for towel, and cup- board below for foul water • - ... jg5 LIII. Ditto, cylinder wafh-hand, with water ciftern at top, and glafs in center, leaden pipe to convey off the foul water into a drawer behind for that purpofe ; the bottom part contains alfo a bidet and two plain drawers - 412 LV. Ditto, tripods for candles, in white or all gold, with figures fupporting the lights _ _ _ . _ - 416 SOFAS. XXXV. Sofa witli three loofe cufiiions at the back, and -ornamented top-rail for japanning - - - - - 388 X. Appendix. — Sofa, the back in three compartments covered with filk, and white and gold frames - - - - 16 LII. Additional nnv Plates. — Sofa in the manner of the Turks, with glafs in center, loofe cufhions all round, and the feat made low - - " 57 STEPS. XII. Appendix. — Steps for large library, with folding hand-rail, and a noting delk at top, the whole folded and inclofed in a Library table. - - 20 XXII. Ditto, ,* w ^ 64a7